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uniformly measurable function

См. также в других словарях:

  • probability theory — Math., Statistics. the theory of analyzing and making statements concerning the probability of the occurrence of uncertain events. Cf. probability (def. 4). [1830 40] * * * Branch of mathematics that deals with analysis of random events.… …   Universalium

  • Dominated convergence theorem — In measure theory, Lebesgue s dominated convergence theorem provides sufficient conditions under which two limit processes commute, namely Lebesgue integration and almost everywhere convergence of a sequence of functions. The dominated… …   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

  • Hilbert space — For the Hilbert space filling curve, see Hilbert curve. Hilbert spaces can be used to study the harmonics of vibrating strings. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It… …   Wikipedia

  • Lebesgue integration — In mathematics, the integral of a non negative function can be regarded in the simplest case as the area between the graph of that function and the x axis. Lebesgue integration is a mathematical construction that extends the integral to a larger… …   Wikipedia

  • Modulus of continuity — In mathematical analysis, a modulus of continuity is a function used to measure quantitatively the uniform continuity of functions. So, a function admits ω as a modulus of continuity if and only if for all x and y in the domain of f. Since moduli …   Wikipedia

  • Empirical measure — In probability theory, an empirical measure is a random measure arising from a particular realization of a (usually finite) sequence of random variables. The precise definition is found below. Empirical measures are relevant to mathematical… …   Wikipedia

  • Egorov's theorem — In measure theory, an area of mathematics, Egorov s theorem establishes a condition for the uniform convergence of a pointwise convergent sequence of measurable functions. The theorem is named after Dmitri Egorov, a Russian physicist and geometer …   Wikipedia

  • Probability distribution — This article is about probability distribution. For generalized functions in mathematical analysis, see Distribution (mathematics). For other uses, see Distribution (disambiguation). In probability theory, a probability mass, probability density …   Wikipedia

  • Absolute continuity — In mathematics, the relationship between the two central operations of calculus, differentiation and integration, stated by fundamental theorem of calculus in the framework of Riemann integration, is generalized in several directions, using… …   Wikipedia

  • Itō diffusion — In mathematics mdash; specifically, in stochastic analysis mdash; an Itō diffusion is a solution to a specific type of stochastic differential equation. Itō diffusions are named after the Japanese mathematician Kiyoshi Itō.OverviewA (time… …   Wikipedia

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