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. He showed that the unit interval endowed with the Lebesgue measure has important advantages over general probability spaces, and can be used as a probability space for all practical purposes in probability theory. The theory of standard probability spaces was started by von Neumann in 1932 and shaped by Vladimir Rokhlin in 1940. The dimension of the unit interval is not a concern, 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.
Read more about Standard Probability Space: Short History, Definition, A Criterion of Standardness, Equivalent Definitions, Verifying The Standardness
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