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Difference between revisions of "User:Boris Tsirelson/sandbox1"

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<ref> [http://hea-www.harvard.edu/AstroStat http://hea-www.harvard.edu/AstroStat]; <nowiki> http://www.incagroup.org </nowiki>; <nowiki> http://astrostatistics.psu.edu </nowiki> </ref>
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====Notes====
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<references />
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-------------------------------------------
  
====References====
 
  
 
{|
 
{|
|valign="top"|{{Ref|I}}||   Kiyosi Itô, "Introduction to  probability theory", Cambridge (1984).  &nbsp; {{MR|0777504}}  &nbsp; {{ZBL|0545.60001}}
+
| A || B || C
|-
 
|valign="top"|{{Ref|Ru}}||  Thierry de la Rue, "Espaces de Lebesgue", ''Séminaire de Probabilités  XXVII,'' Lecture Notes in Mathematics, '''1557''' (1993), Springer,  Berlin,  pp. 15–21. &nbsp;  {{MR|1308547}} &nbsp;  {{ZBL|0788.60001}}
 
 
|-
 
|-
|valign="top"|{{Ref|H}}||   Jean  Haezendonck, "Abstract  Lebesgue-Rohlin  spaces",  ''Bull. Soc.  Math.  de Belgique'' '''25'''  (1973), 243–258.  &nbsp;    {{MR|0335733}}  &nbsp;  {{ZBL|0308.60006}}
+
| X || Y || Z
|-
 
|valign="top"|{{Ref|HN}}||  P.R. Halmos, J. von Neumann, "Operator  methods in classical mechanics,  II", ''Annals of Mathematics (2)''  '''43''' (1942), 332–350.    &nbsp;  {{MR|0006617}} &nbsp;    {{ZBL|0063.01888}}
 
|-
 
|valign="top"|{{Ref|Ro}}||  V.A. Rokhlin, (1962), "On the fundamental ideas of measure theory",  ''Translations (American Mathematical Society) Series 1,'' 10 (1962),  1–54. &nbsp; {{MR|0047744}} &nbsp; Translated from Russian:  Рохлин, В. А. (1949), "Об основных понятиях теории меры", Математический  Сборник (Новая Серия) 25(67): 107–150. &nbsp; {{MR|0030584}}
 
 
|}
 
|}
  
  
{|
+
 
|valign="top"|{{Ref|P}}||  Karl Petersen, "Ergodic theory", Cambridge (1983). &nbsp; {{MR|0833286}} &nbsp; {{ZBL|0507.28010}}
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-----------------------------------------
|-
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-----------------------------------------
|valign="top"|{{Ref|H1}}|| P.R. Halmos, "Measure theory", Van Nostrand (1950). &nbsp; {{MR|0033869}} &nbsp; {{ZBL|0040.16802}}
+
 
|-
+
$\newcommand*{\longhookrightarrow}{\lhook\joinrel\relbar\joinrel\rightarrow}$
|valign="top"|{{Ref|H2}}|| P.R. Halmos, "Lectures on ergodic theory", Math. Soc. Japan (1956). &nbsp; {{MR|0097489}} &nbsp; {{ZBL|0073.09302}}
+
 
|-
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<asy>
|valign="top"|{{Ref|G}}|| Eli Glasner, "Ergodic theory via joinings", Amer. Math. Soc. (2003). &nbsp; {{MR|1958753}} &nbsp; {{ZBL|1038.37002}}
+
size(100,100);
|-
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label(scale(1.7)*'$T(\\Sigma)\hookrightarrow T(\\Sigma,X)$',(0,0));
|valign="top"|{{Ref|K}}|| Alexander  S.  Kechris, "Classical      descriptive set theory", Springer-Verlag  (1995). &nbsp;     {{MR|1321597}} &nbsp; {{ZBL|0819.04002}}
+
</asy>
|-
+
 
|valign="top"|{{Ref|F}}||  D.H. Fremlin, "Measure theory",  Torres  Fremlin, Colchester. Vol. 1:  2004 &nbsp; {{MR|2462519}}  &nbsp;   {{ZBL|1162.28001}}; Vol. 2:  2003  &nbsp; {{MR|2462280}}   &nbsp; {{ZBL|1165.28001}}; Vol. 3:  2004 &nbsp;    {{MR|2459668}}  &nbsp; {{ZBL|1165.28002}}; Vol. 4:  2006  &nbsp;   {{MR|2462372}} &nbsp; {{ZBL|1166.28001}}
+
<asy>
|-
+
size(220,220);
|valign="top"|{{Ref|S}}|| I.E. Segal, "Abstract probability spaces and a theorem of Kolmogoroff",  ''Amer. J. Math.'' '''76''' (1954), 721–732. &nbsp; {{MR|0063602}} &nbsp; {{ZBL|0056.12301}}
+
 
|-
+
import math;
|valign="top"|{{Ref|D}}|| L.E. Dubins, "Generalized random variables",  ''Trans. Amer. Math. Soc.'' '''84''' (1957), 273–309. &nbsp; {{MR|0085326}} &nbsp; {{ZBL|0078.31003}}
+
 
|-
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int kmax=40;
|valign="top"|{{Ref|W}}|| David Williams, "Probability with martingales", Cambridge  (1991). &nbsp;   {{MR|1155402}} &nbsp; {{ZBL|0722.60001}}
+
 
|-
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guide g;
|valign="top"|{{Ref|C}}|| Constantin Carathėodory, "Die homomorphieen von Somen und die Multiplikation von  Inhaltsfunktionen" (German), ''Annali della R. Scuola Normale Superiore di Pisa (Ser. 2)'' '''8''' (1939), 105–130.  &nbsp; {{MR|1556820}} &nbsp;  {{ZBL|0021.11403}}
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for (int k=-kmax; k<=kmax; ++k) {
|-
+
   real phi = 0.2*k*pi;
|valign="top"|{{Ref|HN}}|| P.R. Halmos, J. von Neumann, "Operator methods in classical mechanics, II", ''Annals of Mathematics (2)'' '''43''' (1942), 332–350.  &nbsp;   {{MR|0006617}} &nbsp;  {{ZBL|0063.01888}}
+
   real rho = 1;
|}
+
  if (k!=0) {
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    rho = sin(phi)/phi;
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  }
 +
  pair z=rho*expi(phi);
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  g=g..z;
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}
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draw (g);
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defaultpen(0.75);
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draw ( (0,0)--(1.3,0), dotted, Arrow(SimpleHead,5) );
 +
dot ( (1,0) );
 +
label ( "$a$", (1,0), NE );
 +
 
 +
</asy>

Latest revision as of 07:12, 13 March 2016

[1]

Notes

  1. http://hea-www.harvard.edu/AstroStat; http://www.incagroup.org ; http://astrostatistics.psu.edu


A B C
X Y Z




$\newcommand*{\longhookrightarrow}{\lhook\joinrel\relbar\joinrel\rightarrow}$

How to Cite This Entry:
Boris Tsirelson/sandbox1. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Boris_Tsirelson/sandbox1&oldid=24217