Standard Probability Space
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High Quality Content by WIKIPEDIA articles! In probability theory, a standard probability space (called also 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 dimension of the unit interval is not a concern, which was clear already to Norbert Wiener...
High Quality Content by WIKIPEDIA articles! In probability theory, a standard probability space (called also 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 dimension of the unit interval is not a concern, which 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.
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