# User:Boris Tsirelson

My homepage at School of Mathematics, Tel Aviv University.

My user page on Wikipedia.

My research interests are in probability.

## Contents

## My contributions

Measurable space (30,000+ views); Standard Borel space (7,000+ views); Analytic Borel space (3,000+ views); Universally measurable (3,000+ views); Measure space (10,000+ views); Standard probability space (3,000+ views); Measure algebra (measure theory) (4,000+ 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 1860+ articles viewed 1860+ 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.

##### New articles

##### Recently updated

##### Recently discussed

##### Most popular

- Inverse function (44293 views)
- Analytic function (35469 views)
- Mathematical symbols (32963 views)
- Measurable space (30700 views)
- Parallel transport (30279 views)
- Function of bounded variation (28503 views)
- Upper and lower limits (19086 views)
- Absolute continuity (15598 views)
- Newton-Leibniz formula (15468 views)
- Borel function (13542 views)

## Notes to myself

### Internal links

Talk:EoM:This project + Help:MSC Templates + User:Ulf Rehmann/Predefined TeX Macros + 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

- 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 links

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

Claude Henri Picard (Claudeh5)

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

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

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). {{MR|1321597}} {{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. {{MR|0089999}} {{ZBL|0082.11201}}

|}

#### Article

*Also: standard measurable space*

{{MSC|03E15|28A05,54H05}}

[[Category:Descriptive set theory]]

[[Category:Classical measure theory]]

$ \newcommand...$

A Borel space is called **standard** if...

{{MSC|60-01|60F15,60F20}}

{{DEF}}

This is a "wanted page". It was proposed that an entry with this title should be included.

{{TEX|want}}

*subtitle*

{{MSC|...}}

[[Category:...]]

{{TEX|done}}

#### Category

* {{MSC|60J10}}

[[Category:Markov processes]]

* {{MSC|60Jxx}}

[[Category:Probability theory and stochastic processes]]

* {{MSC|60}}

[[Category:Probability and statistics]]

#### Talk

- And please sign your messages (on talk pages) by four tildas: ~~~~.

**How to Cite This Entry:**

Boris Tsirelson.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Boris_Tsirelson&oldid=35700