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measurability theorem

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  • Donsker's theorem — In probability theory, Donsker s theorem, named after M. D. Donsker, identifies a certain stochastic process as a limit of empirical processes. It is sometimes called the functional central limit theorem. A centered and scaled version of… …   Wikipedia

  • Alexandra Bellow — (1935 ndash;) is a mathematician who has made substantial contributions to the fields of ergodic theory, probability and analysis. BiographyShe was born in Bucharest, Romania, as Alexandra Bagdasar. Her parents were both physicians. Her mother,… …   Wikipedia

  • Standard probability space — In probability theory, a standard probability space (called also Lebesgue Rokhlin probability space) is a probability space satisfying certain assumptions introduced by Vladimir Rokhlin in 1940 [1] . He showed that the unit interval endowed with… …   Wikipedia

  • Weakly measurable function — See also= In mathematics mdash; specifically, in functional analysis mdash; a weakly measurable function taking values in a Banach space is a function whose composition with any element of the dual space is a measurable function in the usual… …   Wikipedia

  • Characterizations of the exponential function — In mathematics, the exponential function can be characterized in many ways. The following characterizations (definitions) are most common. This article discusses why each characterization makes sense, and why the characterizations are independent …   Wikipedia

  • Congruence lattice problem — In mathematics, the congruence lattice problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of some other lattice. The problem was posed by Robert P. Dilworth, and for many years it was one of the most …   Wikipedia

  • Axiom of choice — This article is about the mathematical concept. For the band named after it, see Axiom of Choice (band). In mathematics, the axiom of choice, or AC, is an axiom of set theory stating that for every family of nonempty sets there exists a family of …   Wikipedia

  • Measurable function — In mathematics, particularly in measure theory, measurable functions are structure preserving functions between measurable spaces; as such, they form a natural context for the theory of integration. Specifically, a function between measurable… …   Wikipedia

  • Constructivism (mathematics) — In the philosophy of mathematics, constructivism asserts that it is necessary to find (or construct ) a mathematical object to prove that it exists. When one assumes that an object does not exist and derives a contradiction from that assumption,… …   Wikipedia

  • Outer measure — In mathematics, in particular in measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical conditions. A general theory… …   Wikipedia

  • Conditional expectation — In probability theory, a conditional expectation (also known as conditional expected value or conditional mean) is the expected value of a real random variable with respect to a conditional probability distribution. The concept of conditional… …   Wikipedia

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