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* [http://www.tau.ac.il/~tsirel/ My website]
+
My [http://www.tau.ac.il/~tsirel/ homepage] at School of Mathematics, Tel Aviv University.
* My user pages on other wikis: [http://en.wikipedia.org/wiki/User:Tsirel Wikipedia], [http://en.citizendium.org/wiki/User:Boris_Tsirelson Citizendium], [http://knowino.org/wiki/User:Boris_Tsirelson Knowino]
+
 
 +
My [http://en.wikipedia.org/wiki/User:Tsirel user page] on Wikipedia.
 +
 
 +
My research interests are in [[:Category:Probability theory and stochastic processes|probability]].
 +
 
 +
* ''Boris has [https://en-exact-sciences.tau.ac.il/math/Tsirelsonborisen passed away] on January 21, 2020. May he rest in peace.''
  
 
==My contributions==
 
==My contributions==
  
[[Measurable space]]
+
[[Measurable space]] (50,000+ views);
+ [[Standard Borel space]]
+
[[Standard Borel space]] (12,000+ views);
 +
[[Analytic Borel space]] (5,000+ views);
 +
[[Universally measurable]] (5,000+ views);
 +
[[Measure space]] (20,000+ views);
 +
[[Standard probability space]] (6,000+ views);
 +
[[Measure algebra (measure theory)]] (7,000+ views).
 +
 
 +
===Wanted===
 +
 
 +
[[Random matrix]]
 +
+ [[SLE]]
 +
+ [[Gaussian measure]]
 +
 
 +
And maybe:
 +
[[Borel equivalence relation]] (see [http://en.wikipedia.org/wiki/Talk:Borel_equivalence_relation WP])
 +
 
 +
===Require revision===
 +
 
 +
[[Bell inequalities]]
 +
+ [[Probability of large deviations]]
  
 
==Some statistics==
 
==Some statistics==
  
We have 40+ articles with 40+ views each. [http://www.encyclopediaofmath.org/index.php/Special:PopularPages?limit=11&offset=39]
+
We have 2590+ articles viewed 2590+ times each. [https://www.encyclopediaofmath.org/index.php/Special:PopularPages?limit=21&offset=2589]
 +
 
 +
History: Dec 2011: 40×40; Jan 2012: 60×60; Feb 2012: 90×90; Mar 2012: 140×140; Apr 2012: 200×200; May 2012: 250×250; Jun 2012: 320×320; Jul 2012: 370×370; Aug 2012: 410×410; Sep 2012: 460×460; Oct 2012: 520×520; Nov 2012: 590×590; Dec 2012: 650×650; Jan 2013: 710×710; Feb 2013: 760×760; Mar 2013: 820×820; Apr 2013: 890×890; May 2013: 940×940; Jun 2013: 990×990; Jul 2013: 1040×1040; Aug 2013: 1080×1080; Sep 2013: 1130×1130; Oct 2013: 1170×1170; Nov 2013: 1220×1220; Dec 2013: 1260×1260; Jan 2014: 1300×1300; Feb 2014: 1330×1330; Mar 2014: 1380×1380; Apr 2014: 1420×1420; May 2014: 1480×1480; Jun 2014: 1520×1520; Jul 2014: 1600×1600; Aug 2014: 1640×1640; Sep 2014: 1700×1700; Oct 2014: 1760×1760; Nov 2014: 1800×1800; Dec 2014: 1860×1860; Jan 2015: 1920×1920; Feb 2015: 1960×1960; Mar 2015: 2020×2020; Apr 2015: 2080×2080; May 2015: 2140×2140; June 2015: 2180×2180; Aug 2015: 2260×2260; Sep 2015: 2280×2280; Oct 2015: 2290×2290; Nov 2015: 2300×2300; Dec 2015: 2310×2310; Jan 2016: 2320×2320; Feb 2016: 2340×2340; Jun 2016: 2400×2400; Oct 2016: 2480×2480; Feb 2017: 2590x2590.
 +
 
 +
<DynamicArticleList>
 +
  title=New articles
 +
count=10
 +
categoryRoot=Mathematics
 +
</DynamicArticleList>
 +
 
 +
<DynamicArticleList>
 +
  title=Recently updated
 +
  type=update
 +
count=10
 +
categoryRoot=Mathematics
 +
</DynamicArticleList>
 +
 
 +
<DynamicArticleList>
 +
  title=Recently discussed
 +
  type=discussion
 +
count=10
 +
categoryRoot=Mathematics
 +
</DynamicArticleList>
 +
 
 +
<DynamicArticleList>
 +
  title=Most popular
 +
  type=hot
 +
  count=10
 +
categoryRoot=Mathematics
 +
</DynamicArticleList>
 +
 
 +
==Notes to myself==
 +
 
 +
Measurable space: 48149 views at 14 November 2015; 49,116 views at 1 July 2016; 52,310 views at 7 March 2017.
 +
Rigid analytic space: 2298 views at 14 November 2015; 2,454 views at 1 July 2016; 2,749 views at 7 March 2017.
 +
 
 +
===Internal links===
 +
[[Talk:EoM:This project]]
 +
+ [[Help:MSC Templates]]
 +
+ [[User:Ulf Rehmann/Predefined TeX Macros]]
 +
+ [[Help:HowTo EoM]]
 +
+ [[User talk:Ulf Rehmann]]
 +
+ [[User talk:Nbrothers]]
 +
+ [[Encyclopedia of Mathematics:Administrators]]
 +
+ [https://www.encyclopediaofmath.org/index.php?title=Special%3APrefixIndex&prefix=&namespace=12 all help pages]
  
==Links==
 
===Internal===
 
 
[[Special:PopularPages|Popular pages]]
 
[[Special:PopularPages|Popular pages]]
 
+ [[Special:Statistics|Statistics]]
 
+ [[Special:Statistics|Statistics]]
Line 21: Line 87:
 
+ [[Special:Categories|Categories]]
 
+ [[Special:Categories|Categories]]
 
+ [[Special:WantedCategories|Wanted categories]]
 
+ [[Special:WantedCategories|Wanted categories]]
+ [http://www.encyclopediaofmath.org/index.php?title=Special%3AAllPages&from=&to=&namespace=10 Templates]
+
+ [[:Category:Deficient]]
 +
+ [https://www.encyclopediaofmath.org/index.php?title=Special%3AAllPages&from=&to=&namespace=10 Templates]
 +
 
 +
Non-Asy:
 +
[[Hysteron]]
 +
+ [[Ellipse]]
 +
+ [[Automata, methods of specification of]]
 +
+ [[Pascal geometry]]
 +
+ [[Braided group]]
 +
+ [[Differential geometry]]
 +
+ [[Hypergraph]]
 +
+ [[Torus knot]]
 +
+ [[Equal content and equal shape, figures of]]
 +
+ [[System of subvarieties]]
 +
 
 +
Partially Asy: [[Wild knot]]
 +
 
 +
Asy: [[Sinusoid]]
 +
+ [[Cantor ternary function]]
 +
+ [[Caustic]]
 +
+ [[Non-precise data]]
 +
+ [[Golden ratio]]
 +
+ [[Kolmogorov test]]
 +
+ [[Power function]]
 +
+ [[Sinusoidal spiral]]
 +
 
 +
===Maybe need more attention===
 +
* [[Special:Contributions/Ginachoi002]]
 +
* [[Lindelöf hypothesis]]
 +
* [[Cullinane diamond theorem]] (refs format)
 +
* [[Genetic Algorithms]] (title capitalization; refs format)
 +
* [[Modulus in algebraic number theory]] + [[Continuant]] + [[ABC conjecture]] (refs format)
 +
* [[Lindenbaum method]] (refs format)
 +
* [[Arithmetization of analysis]] (formulas format;  refs format)
  
===External===
+
===External links===
 
[http://msc2010.org/mscwiki/index.php?title=Main_Page MSC wiki]
 
[http://msc2010.org/mscwiki/index.php?title=Main_Page MSC wiki]
 +
+ [http://www.mediawiki.org/wiki/Extension:QuestyCaptcha QuestyCaptcha]
 +
+ [http://en.wikipedia.org/wiki/Wikipedia:WikiProject_Spam WikiProject Spam]
 +
+ [http://en.wikipedia.org/wiki/User:XLinkBot WP:XLinkBot]
 +
+ [http://www.communitywiki.org/WikiSpam WikiSpam]
 +
+ [http://asymptote.sourceforge.net/ Asymptote]
 +
 +
[http://ncatlab.org/nlab/show/HomePage nLab]
 +
+ [http://texnicalstuff.blogspot.co.il/p/table-of-contents.html TeX-nical Stuff]
  
===Probability===
+
[http://ref.subwiki.org/wiki/Main_Page Subject Wikis]
  
 +
[https://meta.wikimedia.org/wiki/Grants:IdeaLab/PlanetMath_Books_Project PlanetMath Books Project]
 +
 +
[https://fr.wikipedia.org/wiki/Utilisateur:Claudeh5?setlang=en Claude Henri Picard (Claudeh5)]
 +
 +
===Probability (and related) articles===
 
[[Absorbing state]]
 
[[Absorbing state]]
 
+ [[Approximation by periodic transformations]]
 
+ [[Approximation by periodic transformations]]
Line 56: Line 168:
 
+ [[Chebyshev inequality in probability theory]]
 
+ [[Chebyshev inequality in probability theory]]
 
+ [[Continuous distribution]]
 
+ [[Continuous distribution]]
 +
+ [[Continuous flow]]
 
+ [[Convergence, types of]]
 
+ [[Convergence, types of]]
 
+ [[Convergence in distribution]]
 
+ [[Convergence in distribution]]
Line 77: Line 190:
 
+ [[Ergodicity]]
 
+ [[Ergodicity]]
 
+ [[Exponential distribution]]
 
+ [[Exponential distribution]]
+ [[Extrapolation algorithm]]
 
  
 
[[Feller process]]
 
[[Feller process]]
Line 85: Line 197:
 
[[Galton–Watson process]]
 
[[Galton–Watson process]]
 
+ [[Gaussian process]]
 
+ [[Gaussian process]]
+ [[Generating function]]
 
 
+ [[Geometric distribution]]
 
+ [[Geometric distribution]]
 
+ [[Gram–Charlier series]]
 
+ [[Gram–Charlier series]]
Line 96: Line 207:
 
+ [[Kolmogorov–Smirnov test]]
 
+ [[Kolmogorov–Smirnov test]]
  
Laplace theorem
+
[[Laplace theorem]]
Law of large numbers
+
+ [[Law of large numbers]]
Law of the iterated logarithm
+
+ [[Law of the iterated logarithm]]
Lebesgue integral
+
+ [[Lebesgue integral]]
Lebesgue space
+
+ [[Limit theorems]]
Limit theorems
+
+ [[Lévy canonical representation]]
Lévy canonical representation
+
+ [[Lévy metric]]
Lévy metric
+
 
Markov chain
+
[[Markov chain]]
Markov chain, class of zero states of a
+
+ [[Markov chain, class of zero states of a]]
Markov chain, decomposable
+
+ [[Markov chain, decomposable]]
Markov chain, generalized
+
+ [[Markov chain, generalized]]
Markov chain, non-decomposable
+
+ [[Markov chain, non-decomposable]]
Markov chain, periodic
+
+ [[Markov chain, periodic]]
Markov chain, recurrent
+
+ [[Markov chain, recurrent]]
Markov moment
+
+ [[Markov moment]]
Markov process
+
+ [[Markov process]]
Markov property
+
+ [[Markov property]]
Martingale
+
+ [[Martingale]]
Mathematical expectation
+
+ [[Mathematical expectation]]
Mathematical statistics
+
+ [[Mathematical statistics]]
Maximal ergodic theorem
+
+ [[Maximal ergodic theorem]]
Measurable flow
+
+ [[Measurable flow]]
Measurable function
+
+ [[Measurable function]]
Measurable space
+
+ [[Measurable space]]
Measure-preserving transformation
+
+ [[Measure-preserving transformation]]
Median (in statistics)
+
+ [[Median (in statistics)]]
Metric isomorphism
+
+ [[Metric isomorphism]]
Metric transitivity
+
+ [[Metric transitivity]]
Mixing
+
+ [[Mixing]]
Multinomial distribution
+
+ [[Multinomial distribution]]
Normal distribution
+
 
Normal number
+
[[Normal distribution]]
Operator ergodic theorem
+
+ [[Normal number]]
Ornstein–Chacon ergodic theorem
 
Poisson distribution
 
Poisson process
 
Poisson theorem
 
Probabilistic metric space
 
Probability
 
Probability distribution
 
Probability measure
 
Probability of large deviations
 
Probability space
 
Probability theory
 
Quantile
 
Random variable
 
Separable process
 
Sequential analysis
 
Serial scheme
 
Spectrum of a dynamical system
 
Stable distribution
 
Standard Borel space
 
Stationary distribution
 
Stationary stochastic process
 
Statistical physics, mathematical problems in
 
Stochastic differential equation
 
Stochastic equivalence
 
Stochastic indistinguishability
 
Stochastic integral
 
Stochastic matrix
 
Stochastic process
 
Stochastic process with independent increments
 
Stochastic process with stationary increments
 
Strange attractor
 
Strong law of large numbers
 
Tamagawa number
 
Transition-operator semi-group
 
Transition function
 
Transition with prohibitions
 
Triangular array
 
Uniform distribution
 
Von Neumann ergodic theorem
 
Weak convergence of probability measures
 
Wiener process
 
  
==Know-how==
+
[[Operator ergodic theorem]]
 +
+ [[Ornstein–Chacon ergodic theorem]]
 +
 
 +
[[Poisson distribution]]
 +
+ [[Poisson process]]
 +
+ [[Poisson theorem]]
 +
+ [[Probabilistic metric space]]
 +
+ [[Probability]]
 +
+ [[Probability distribution]]
 +
+ [[Probability measure]]
 +
+ [[Probability of large deviations]]
 +
+ [[Probability space]]
 +
+ [[Probability theory]]
 +
 
 +
[[Quantile]]
 +
 
 +
[[Random variable]]
 +
 
 +
[[Separable process]]
 +
+ [[Sequential analysis]]
 +
+ [[Serial scheme]]
 +
+ [[Spectrum of a dynamical system]]
 +
+ [[Stable distribution]]
 +
+ [[Standard Borel space]]
 +
+ [[Stationary distribution]]
 +
+ [[Stationary stochastic process]]
 +
+ [[Statistical physics, mathematical problems in]]
 +
+ [[Stochastic differential equation]]
 +
+ [[Stochastic equivalence]]
 +
+ [[Stochastic indistinguishability]]
 +
+ [[Stochastic integral]]
 +
+ [[Stochastic matrix]]
 +
+ [[Stochastic process]]
 +
+ [[Stochastic process with independent increments]]
 +
+ [[Stochastic process with stationary increments]]
 +
+ [[Strange attractor]]
 +
+ [[Strong law of large numbers]]
 +
 
 +
[[Transition-operator semi-group]]
 +
+ [[Transition function]]
 +
+ [[Transition with prohibitions]]
 +
+ [[Triangular array]]
 +
 
 +
[[Uniform distribution]]
 +
 
 +
[[Variance]]
 +
+ [[Von Neumann ergodic theorem]]
 +
 
 +
[[Weak convergence of probability measures]]
 +
+ [[Wiener process]]
 +
---------------
 +
[[Absolute continuity]]
 +
+ [[Absolutely continuous measures]]
 +
+ [[Accessible random variable]]
 +
+ [[Additive function]]
 +
+ [[Additive noise]]
 +
+ [[Additive stochastic process]]
 +
+ [[Almost-everywhere]]
 +
+ [[A posteriori probability]]
 +
+ [[A priori probability]]
 +
+ [[Asymmetry coefficient]]
 +
+ [[Asymmetry of a distribution]]
 +
+ [[Atomic distribution]]
 +
+ [[Automaton, probabilistic]]
 +
+ [[Auto-correlation]]
 +
+ [[Autocovariance]]
 +
+ [[Auto-regression]]
 +
+ [[Auto-regressive process]]
 +
+ [[Berry-Esseen inequality]]
 +
+ [[Birth-and-death process]]
 +
+ [[Einstein-Smoluchowski equation]]
 +
+ [[Independence]]
 +
+ [[Kolmogorov inequality]]
 +
+ [[Lattice distribution]]
 +
+ [[Lebesgue integral‎]]
 +
+ [[Non-atomic measure]]
 +
+ [[Pascal distribution]]
 +
+ [[Recurrent events]]
 +
+ [[Special functions‎]]
 +
+ [[Truncated distribution]]
 +
 
 +
===Know-how===
 +
 
 +
Symbol choice: [[Talk:Variance]], [[Talk:Almost-periodic analytic function]], [[Talk:Borel-Cantelli lemma]].
  
 
<nowiki>#REDIRECT[[]]</nowiki>
 
<nowiki>#REDIRECT[[]]</nowiki>
  
<nowiki>{{User:Rehmann/sandbox/MSC|60J10|}}</nowiki> (for now)
+
<nowiki>{{Anchor|countably separated}}</nowiki>
 +
 
 +
<nowiki>$\int f(x)\rd x$</nowiki> &nbsp; $\int f(x)\rd x$
 +
 
 +
<nowiki>$\int f(x)\,\mu(\!\rd x)$</nowiki> &nbsp; $\int f(x)\,\mu(\!\rd x)$
 +
 
 +
<nowiki>See {{Cite|K|Sect. 12.B}}.</nowiki>
 +
 
 +
<nowiki>{|</nowiki><br />
 +
<nowiki>|valign="top"|{{Ref|K}}|| Alexander S.  Kechris, "Classical  descriptive set theory", Springer-Verlag (1995). &amp;nbsp;  {{MR|1321597}} &amp;nbsp; {{ZBL|0819.04002}</nowiki><br />
 +
<nowiki>|-</nowiki><br />
 +
<nowiki>|valign="top"|{{Ref|M}}||  George W.  Mackey,  "Borel structure in groups and their duals",  ''Trans.  Amer.  Math. Soc.''  '''85''' (1957), 134–165. &amp;nbsp; {{MR|0089999}} &amp;nbsp; {{ZBL|0082.11201}}</nowiki><br />
 +
<nowiki>|}</nowiki>
 +
 
 +
 
 +
====Article====
 +
''Also: standard measurable space''
 +
 
 +
<nowiki>{{MSC|03E15|28A05,54H05}}</nowiki>
 +
 
 +
<nowiki>[[Category:Descriptive set theory]]</nowiki><br>
 +
<nowiki>[[Category:Classical measure theory]]</nowiki>
 +
 
 +
<nowiki>$ \newcommand...$</nowiki><br>
 +
A Borel space is called '''standard''' if...
 +
 
 +
-----------------------------------------------------
 +
 
 +
<nowiki>{{MSC|60-01|60F15,60F20}}</nowiki>
 +
 
 +
-----------------------------------------------------
 +
 
 +
<nowiki>{{DEF}}</nowiki><br>
 +
This is a "wanted page". It was proposed that an entry with this title should be included.<br>
 +
<nowiki>{{TEX|want}}</nowiki><br>
 +
''subtitle''<br>
 +
<nowiki>{{MSC|...}}</nowiki><br>
 +
<nowiki>[[Category:...]]</nowiki><br>
 +
<nowiki>{{TEX|done}}</nowiki><br>
 +
 
 +
====Category====
 +
 
 +
<nowiki>* {{MSC|60J10}}</nowiki>
 +
 
 +
<nowiki>[[Category:Markov processes]]</nowiki>
 +
 
 +
--------------------------------------
 +
 
 +
<nowiki>* {{MSC|60Jxx}}</nowiki>
 +
 
 +
<nowiki>[[Category:Probability theory and stochastic processes]]</nowiki>
 +
 
 +
--------------------------------------
 +
 
 +
<nowiki>* {{MSC|60}}</nowiki>
 +
 
 +
<nowiki>[[Category:Probability and statistics]]</nowiki>
 +
 
 +
====Talk====
  
<nowiki>{{User:Boris Tsirelson/C1|60Jxx}} (MSC2010 code)</nowiki> (for now)
+
: And please sign your messages (on talk pages) with four tildas: <nowiki>~~~~</nowiki>.

Latest revision as of 05:59, 19 January 2022

My homepage at School of Mathematics, Tel Aviv University.

My user page on Wikipedia.

My research interests are in probability.

  • Boris has passed away on January 21, 2020. May he rest in peace.

My contributions

Measurable space (50,000+ views); Standard Borel space (12,000+ views); Analytic Borel space (5,000+ views); Universally measurable (5,000+ views); Measure space (20,000+ views); Standard probability space (6,000+ views); Measure algebra (measure theory) (7,000+ views).

Wanted

Random matrix + SLE + Gaussian measure

And maybe: Borel equivalence relation (see WP)

Require revision

Bell inequalities + Probability of large deviations

Some statistics

We have 2590+ articles viewed 2590+ times each. [1]

History: Dec 2011: 40×40; Jan 2012: 60×60; Feb 2012: 90×90; Mar 2012: 140×140; Apr 2012: 200×200; May 2012: 250×250; Jun 2012: 320×320; Jul 2012: 370×370; Aug 2012: 410×410; Sep 2012: 460×460; Oct 2012: 520×520; Nov 2012: 590×590; Dec 2012: 650×650; Jan 2013: 710×710; Feb 2013: 760×760; Mar 2013: 820×820; Apr 2013: 890×890; May 2013: 940×940; Jun 2013: 990×990; Jul 2013: 1040×1040; Aug 2013: 1080×1080; Sep 2013: 1130×1130; Oct 2013: 1170×1170; Nov 2013: 1220×1220; Dec 2013: 1260×1260; Jan 2014: 1300×1300; Feb 2014: 1330×1330; Mar 2014: 1380×1380; Apr 2014: 1420×1420; May 2014: 1480×1480; Jun 2014: 1520×1520; Jul 2014: 1600×1600; Aug 2014: 1640×1640; Sep 2014: 1700×1700; Oct 2014: 1760×1760; Nov 2014: 1800×1800; Dec 2014: 1860×1860; Jan 2015: 1920×1920; Feb 2015: 1960×1960; Mar 2015: 2020×2020; Apr 2015: 2080×2080; May 2015: 2140×2140; June 2015: 2180×2180; Aug 2015: 2260×2260; Sep 2015: 2280×2280; Oct 2015: 2290×2290; Nov 2015: 2300×2300; Dec 2015: 2310×2310; Jan 2016: 2320×2320; Feb 2016: 2340×2340; Jun 2016: 2400×2400; Oct 2016: 2480×2480; Feb 2017: 2590x2590.

<DynamicArticleList>

 title=New articles
count=10
categoryRoot=Mathematics

</DynamicArticleList>

<DynamicArticleList>

 title=Recently updated
 type=update
count=10
categoryRoot=Mathematics

</DynamicArticleList>

<DynamicArticleList>

 title=Recently discussed
 type=discussion
count=10
categoryRoot=Mathematics

</DynamicArticleList>

<DynamicArticleList>

 title=Most popular
 type=hot
 count=10
categoryRoot=Mathematics

</DynamicArticleList>

Notes to myself

Measurable space: 48149 views at 14 November 2015; 49,116 views at 1 July 2016; 52,310 views at 7 March 2017. Rigid analytic space: 2298 views at 14 November 2015; 2,454 views at 1 July 2016; 2,749 views at 7 March 2017.

Internal links

Talk:EoM:This project + Help:MSC Templates + User:Ulf Rehmann/Predefined TeX Macros + Help:HowTo EoM + User talk:Ulf Rehmann + User talk:Nbrothers + Encyclopedia of Mathematics:Administrators + all help pages

Popular pages + Statistics + Version

New pages + New users + Categories + Wanted categories + Category:Deficient + Templates

Non-Asy: Hysteron + Ellipse + Automata, methods of specification of + Pascal geometry + Braided group + Differential geometry + Hypergraph + Torus knot + Equal content and equal shape, figures of + System of subvarieties

Partially Asy: Wild knot

Asy: Sinusoid + Cantor ternary function + Caustic + Non-precise data + Golden ratio + Kolmogorov test + Power function + Sinusoidal spiral

Maybe need more attention

External links

MSC wiki + QuestyCaptcha + WikiProject Spam + WP:XLinkBot + WikiSpam + Asymptote

nLab + TeX-nical Stuff

Subject Wikis

PlanetMath Books Project

Claude Henri Picard (Claudeh5)

Probability (and related) articles

Absorbing state + Approximation by periodic transformations + Arcsine distribution + Asymptotic negligibility + Attraction domain of a stable distribution

Baire set + Bellman–Harris process + Bernoulli theorem + Bernoulli trials + Binomial distribution + Birkhoff ergodic theorem + Borel measure + Borel space + Borel strong law of large numbers + Borel–Cantelli lemma + Branching process + Branching process, age-dependent + Branching process with a random medium + Branching process with immigration + Branching processes, regularity of + Brownian motion

Cauchy distribution + Central limit theorem + Characteristic function + Chebyshev inequality in probability theory + Continuous distribution + Continuous flow + Convergence, types of + Convergence in distribution + Convergence in probability + Convergence of measures + Cramér theorem + Cramér–von Mises test

Diffusion process + Discrete distribution + Dispersion + Distribution function + Distributions, convergence of + Dynamical system

Edgeworth series + Elementary flow + Entropy theory of a dynamical system + Ergodic theorem + Ergodic theory + Ergodicity + Exponential distribution

Feller process + Flow (continuous-time dynamical system) + Functional of a Markov process

Galton–Watson process + Gaussian process + Geometric distribution + Gram–Charlier series

Infinitely-divisible distribution

Kolmogorov equation + Kolmogorov test + Kolmogorov–Chapman equation + Kolmogorov–Smirnov test

Laplace theorem + Law of large numbers + Law of the iterated logarithm + Lebesgue integral + Limit theorems + Lévy canonical representation + Lévy metric

Markov chain + Markov chain, class of zero states of a + Markov chain, decomposable + Markov chain, generalized + Markov chain, non-decomposable + Markov chain, periodic + Markov chain, recurrent + Markov moment + Markov process + Markov property + Martingale + Mathematical expectation + Mathematical statistics + Maximal ergodic theorem + Measurable flow + Measurable function + Measurable space + Measure-preserving transformation + Median (in statistics) + Metric isomorphism + Metric transitivity + Mixing + Multinomial distribution

Normal distribution + Normal number

Operator ergodic theorem + Ornstein–Chacon ergodic theorem

Poisson distribution + Poisson process + Poisson theorem + Probabilistic metric space + Probability + Probability distribution + Probability measure + Probability of large deviations + Probability space + Probability theory

Quantile

Random variable

Separable process + Sequential analysis + Serial scheme + Spectrum of a dynamical system + Stable distribution + Standard Borel space + Stationary distribution + Stationary stochastic process + Statistical physics, mathematical problems in + Stochastic differential equation + Stochastic equivalence + Stochastic indistinguishability + Stochastic integral + Stochastic matrix + Stochastic process + Stochastic process with independent increments + Stochastic process with stationary increments + Strange attractor + Strong law of large numbers

Transition-operator semi-group + Transition function + Transition with prohibitions + Triangular array

Uniform distribution

Variance + Von Neumann ergodic theorem

Weak convergence of probability measures + Wiener process


Absolute continuity + Absolutely continuous measures + Accessible random variable + Additive function + Additive noise + Additive stochastic process + Almost-everywhere + A posteriori probability + A priori probability + Asymmetry coefficient + Asymmetry of a distribution + Atomic distribution + Automaton, probabilistic + Auto-correlation + Autocovariance + Auto-regression + Auto-regressive process + Berry-Esseen inequality + Birth-and-death process + Einstein-Smoluchowski equation + Independence + Kolmogorov inequality + Lattice distribution + Lebesgue integral‎ + Non-atomic measure + Pascal distribution + Recurrent events + Special functions‎ + Truncated distribution

Know-how

Symbol choice: Talk:Variance, Talk:Almost-periodic analytic function, Talk:Borel-Cantelli lemma.

#REDIRECT[[]]

{{Anchor|countably separated}}

$\int f(x)\rd x$   $\int f(x)\rd x$

$\int f(x)\,\mu(\!\rd x)$   $\int f(x)\,\mu(\!\rd x)$

See {{Cite|K|Sect. 12.B}}.

{|
|valign="top"|{{Ref|K}}|| Alexander S. Kechris, "Classical descriptive set theory", Springer-Verlag (1995). &nbsp; {{MR|1321597}} &nbsp; {{ZBL|0819.04002}
|-
|valign="top"|{{Ref|M}}|| George W. Mackey, "Borel structure in groups and their duals", ''Trans. Amer. Math. Soc.'' '''85''' (1957), 134–165. &nbsp; {{MR|0089999}} &nbsp; {{ZBL|0082.11201}}
|}


Article

Also: standard measurable space

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[[Category:Descriptive set theory]]
[[Category:Classical measure theory]]

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A Borel space is called standard if...


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[[Category:Markov processes]]


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[[Category:Probability theory and stochastic processes]]


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[[Category:Probability and statistics]]

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How to Cite This Entry:
Boris Tsirelson. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Boris_Tsirelson&oldid=20048