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

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====On terminology====
 
====On terminology====
  
The term "standard probability space" is used in {{Cite|Ito}}. The same, or very similar, notion appears also as "Lebesgue space" {{Cite|Ro}}, {{Cite|Ru}}, {{Cite|P}}, {{Cite|G}},
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The term "standard probability space" is used in {{Cite|I}}. The same, or very similar, notion appears also as: "Lebesgue space" {{Cite|Ro}}, {{Cite|Ru}}, {{Cite|P}}, {{Cite|G}}; "standard Lebesgue space" {{Cite|G}}; "Lebesgue-Rohlin space" {{Cite|H}}, {{Cite|B}}; and "L. R. space" {{Cite|H}}.
  
 
====References====
 
====References====

Revision as of 20:27, 5 April 2012

On terminology

The term "standard probability space" is used in [I]. The same, or very similar, notion appears also as: "Lebesgue space" [Ro], [Ru], [P], [G]; "standard Lebesgue space" [G]; "Lebesgue-Rohlin space" [H], [B]; and "L. R. space" [H].

References

[I] Kiyosi Itô, "Introduction to probability theory", Cambridge (1984).   MR0777504   Zbl 0545.60001
[Ru] Thierry de la Rue, "Espaces de Lebesgue", Séminaire de Probabilités XXVII, Lecture Notes in Mathematics, 1557 (1993), Springer, Berlin, pp. 15–21.   MR1308547   Zbl 0788.60001
[H] Jean Haezendonck, "Abstract Lebesgue-Rohlin spaces", Bull. Soc. Math. de Belgique 25 (1973), 243–258.   MR0335733   Zbl 0308.60006
[HN] P.R. Halmos, J. von Neumann, "Operator methods in classical mechanics, II", Annals of Mathematics (2) 43 (1942), 332–350.   MR0006617   Zbl 0063.01888
[Ro] V.A. Rokhlin, (1962), "On the fundamental ideas of measure theory", Translations (American Mathematical Society) Series 1, 10 (1962), 1–54.   MR0047744   Translated from Russian: Рохлин, В. А. (1949), "Об основных понятиях теории меры", Математический Сборник (Новая Серия) 25(67): 107–150.   MR0030584
[P] Karl Petersen, "Ergodic theory", Cambridge (1983).   MR0833286   Zbl 0507.28010
[G] Eli Glasner, "Ergodic theory via joinings", Amer. Math. Soc. (2003).   MR1958753   Zbl 1038.37002
[B] V.I. Bogachev, "Measure theory", Springer-Verlag (2007).   MR2267655  Zbl 1120.28001
[M] George W. Mackey, "Borel structure in groups and their duals", Trans. Amer. Math. Soc. 85 (1957), 134–165.   MR0089999   Zbl 0082.11201
[M] Paul Malliavin, "Integration and probability", Springer-Verlag (1995).   MR1335234   Zbl 0874.28001
How to Cite This Entry:
Boris Tsirelson/sandbox1. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Boris_Tsirelson/sandbox1&oldid=24225