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In probability theory, a standard probability space, also called Lebesgue–Rokhlin probability space or just Lebesgue space (the latter term is ambiguous) is a probability space satisfying certain assumptions introduced by Vladimir Rokhlin in 1940. Informally, it is a probability space consisting of an interval and/or a finite or countable number of atoms.

Attributes	Values
rdfs:label	Espace probabilisé standard (fr) Standard probability space (en)
rdfs:comment	Un espace probabilisé standard également appelé espace de probabilité de Lebesgue-Rokhlin ou plus simplement espace de Lebesgue est un espace probabilisé satisfaisant certaines hypothèses introduites par Vladimir Rokhlin en 1940. Informellement, il s'agit d'un espace probabiliste composé d'un intervalle et/ou d'un nombre fini ou dénombrable d'atomes. * Portail des probabilités et de la statistique (fr) In probability theory, a standard probability space, also called Lebesgue–Rokhlin probability space or just Lebesgue space (the latter term is ambiguous) is a probability space satisfying certain assumptions introduced by Vladimir Rokhlin in 1940. Informally, it is a probability space consisting of an interval and/or a finite or countable number of atoms. (en)
dcterms:subject	Experiment (probability theory) Measure theory
Wikipage page ID	10406190 (xsd:integer)
Wikipage revision ID	1122963358 (xsd:integer)
Link from a Wikipage to another Wikipage	Cardinality of the continuum Probability distribution Probability space Product topology Product measure Nonmeasurable Almost everywhere Almost surely John von Neumann Descriptive set theory Inner measure Measurable Measure theory Conditional expectation Pushforward measure Experiment (probability theory) Local uniform convergence Complete Boolean algebra Complete measure Function space White noise Lebesgue measure Ergodic theory Norbert Wiener Null set Outer measure Cardinality Isomorphism Probability theory Regular conditional probability Regular measure Inverse function Measure theory Wiener process Dimension Disintegration theorem Borel set Polish space Measure-preserving transformation Hölder's inequality Injective function Metrizable Brownian motion Standard Borel space Unit interval Map (mathematics) Monotone convergence theorem Symmetric difference Probability measure Topological space Lebesgue space (disambiguation) Borel sigma-algebra Conditional distribution Vladimir Rokhlin (Soviet mathematician) Standard normal distribution
Link from a Wikipage to an external page	http://ma.huji.ac.il/~matang02/rohlin.pdf
sameAs	Standard probability space Standard probability space Standard probability space Standard probability space
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harv dbt:No dbt:Short_description dbt:Yes dbt:Harvnb dbt:SpringerEOM
id	Standard_probability_space (en)
last	* (en)
title	Standard probability space (en)
has abstract	Un espace probabilisé standard également appelé espace de probabilité de Lebesgue-Rokhlin ou plus simplement espace de Lebesgue est un espace probabilisé satisfaisant certaines hypothèses introduites par Vladimir Rokhlin en 1940. Informellement, il s'agit d'un espace probabiliste composé d'un intervalle et/ou d'un nombre fini ou dénombrable d'atomes. * Portail des probabilités et de la statistique (fr) In probability theory, a standard probability space, also called Lebesgue–Rokhlin probability space or just Lebesgue space (the latter term is ambiguous) is a probability space satisfying certain assumptions introduced by Vladimir Rokhlin in 1940. Informally, it is a probability space consisting of an interval and/or a finite or countable number of atoms. The theory of standard probability spaces was started by von Neumann in 1932 and shaped by Vladimir Rokhlin in 1940. Rokhlin showed that the unit interval endowed with the Lebesgue measure has important advantages over general probability spaces, yet can be effectively substituted for many of these in probability theory. The dimension of the unit interval is not an obstacle, as was clear already to Norbert Wiener. He constructed the Wiener process (also called Brownian motion) in the form of a measurable map from the unit interval to the space of continuous functions. (en)
gold:hypernym	Space
prov:wasDerivedFrom	wikipedia-en:Standard_probability_space?oldid=1122963358&ns=0
page length (characters) of wiki page	29008 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Standard_probability_space
is Link from a Wikipage to another Wikipage of	Probability space John von Neumann Vladimir Abramovich Rokhlin List of probability topics Equidistributed sequence Equivalent definitions of mathematical structures Bernoulli scheme Alexandra Bellow Kolmogorov's zero–one law Kolmogorov automorphism Baire set Abstract L-space Borel set Catalog of articles in probability theory Standard Borel space Walsh function

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