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- Standard_probability_space abstract "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.".
- Standard_probability_space wikiPageExternalLink rohlin.pdf.
- Standard_probability_space wikiPageID "10406190".
- Standard_probability_space wikiPageLength "28924".
- Standard_probability_space wikiPageOutDegree "70".
- Standard_probability_space wikiPageRevisionID "694661822".
- Standard_probability_space wikiPageWikiLink Almost_surely.
- Standard_probability_space wikiPageWikiLink Borel_set.
- Standard_probability_space wikiPageWikiLink Brownian_motion.
- Standard_probability_space wikiPageWikiLink Cardinality.
- Standard_probability_space wikiPageWikiLink Cardinality_of_the_continuum.
- Standard_probability_space wikiPageWikiLink Category:Measure_theory.
- Standard_probability_space wikiPageWikiLink Category:Probability_theory.
- Standard_probability_space wikiPageWikiLink Complete_Boolean_algebra.
- Standard_probability_space wikiPageWikiLink Complete_measure.
- Standard_probability_space wikiPageWikiLink Conditional_expectation.
- Standard_probability_space wikiPageWikiLink Conditional_probability_distribution.
- Standard_probability_space wikiPageWikiLink Descriptive_set_theory.
- Standard_probability_space wikiPageWikiLink Dimension.
- Standard_probability_space wikiPageWikiLink Disintegration_theorem.
- Standard_probability_space wikiPageWikiLink Ergodic_theory.
- Standard_probability_space wikiPageWikiLink Full_measure.
- Standard_probability_space wikiPageWikiLink Function_space.
- Standard_probability_space wikiPageWikiLink Hxc3xb6lders_inequality.
- Standard_probability_space wikiPageWikiLink Injective_function.
- Standard_probability_space wikiPageWikiLink Inner_measure.
- Standard_probability_space wikiPageWikiLink Inverse_function.
- Standard_probability_space wikiPageWikiLink Isomorphism.
- Standard_probability_space wikiPageWikiLink John_von_Neumann.
- Standard_probability_space wikiPageWikiLink Lebesgue_measure.
- Standard_probability_space wikiPageWikiLink Lebesgue_space.
- Standard_probability_space wikiPageWikiLink Map_(mathematics).
- Standard_probability_space wikiPageWikiLink Measure-preserving_dynamical_system.
- Standard_probability_space wikiPageWikiLink Measure_(mathematics).
- Standard_probability_space wikiPageWikiLink Metrization_theorem.
- Standard_probability_space wikiPageWikiLink Monotone_convergence_theorem.
- Standard_probability_space wikiPageWikiLink Non-measurable_set.
- Standard_probability_space wikiPageWikiLink Norbert_Wiener.
- Standard_probability_space wikiPageWikiLink Normal_distribution.
- Standard_probability_space wikiPageWikiLink Null_set.
- Standard_probability_space wikiPageWikiLink Outer_measure.
- Standard_probability_space wikiPageWikiLink Polish_space.
- Standard_probability_space wikiPageWikiLink Probability_distribution.
- Standard_probability_space wikiPageWikiLink Probability_measure.
- Standard_probability_space wikiPageWikiLink Probability_space.
- Standard_probability_space wikiPageWikiLink Probability_theory.
- Standard_probability_space wikiPageWikiLink Product_measure.
- Standard_probability_space wikiPageWikiLink Product_topology.
- Standard_probability_space wikiPageWikiLink Pushforward_measure.
- Standard_probability_space wikiPageWikiLink Regular_conditional_probability.
- Standard_probability_space wikiPageWikiLink Regular_measure.
- Standard_probability_space wikiPageWikiLink Symmetric_difference.
- Standard_probability_space wikiPageWikiLink Topological_space.
- Standard_probability_space wikiPageWikiLink Uniform_convergence.
- Standard_probability_space wikiPageWikiLink Unit_interval.
- Standard_probability_space wikiPageWikiLink Vladimir_Abramovich_Rokhlin.
- Standard_probability_space wikiPageWikiLink White_noise.
- Standard_probability_space wikiPageWikiLink Wiener_process.
- Standard_probability_space wikiPageWikiLinkText "Lebesgue space".
- Standard_probability_space wikiPageWikiLinkText "Standard probability space".
- Standard_probability_space wikiPageWikiLinkText "a bijective measurable and measure preserving map whose inverse is also measurable and measure preserving".
- Standard_probability_space wikiPageWikiLinkText "isomorphism mod 0".
- Standard_probability_space wikiPageWikiLinkText "isomorphism modulo zero".
- Standard_probability_space wikiPageWikiLinkText "modulo zero isomorphism".
- Standard_probability_space wikiPageWikiLinkText "standard measure space".
- Standard_probability_space wikiPageWikiLinkText "standard probability space".
- Standard_probability_space wikiPageWikiLinkText "standard".
- Standard_probability_space id "Standard_probability_space".
- Standard_probability_space last "*".
- Standard_probability_space title "Standard probability space".
- Standard_probability_space wikiPageUsesTemplate Template:Citation.
- Standard_probability_space wikiPageUsesTemplate Template:Harv.
- Standard_probability_space wikiPageUsesTemplate Template:Harvnb.
- Standard_probability_space wikiPageUsesTemplate Template:No.
- Standard_probability_space wikiPageUsesTemplate Template:SpringerEOM.
- Standard_probability_space wikiPageUsesTemplate Template:Yes.
- Standard_probability_space subject Category:Measure_theory.
- Standard_probability_space subject Category:Probability_theory.
- Standard_probability_space hypernym Space.
- Standard_probability_space type Redirect.
- Standard_probability_space comment "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.".
- Standard_probability_space label "Standard probability space".
- Standard_probability_space sameAs Q7598372.
- Standard_probability_space sameAs m.02qby6l.
- Standard_probability_space sameAs Q7598372.
- Standard_probability_space wasDerivedFrom Standard_probability_space?oldid=694661822.
- Standard_probability_space isPrimaryTopicOf Standard_probability_space.