uniform integrability

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• Uniform integrability — The concept of uniform integrability is an important concept in functional analysis and probability theory. If μ is a finite measure, a subset is said to be uniformly integrable if Rephrased with a probabilistic language, the definition… …   Wikipedia

• Uniform absolute continuity — In mathematical analysis, a collection mathcal{F} of real valued and integrable functions is uniformly absolutely continuous, if for every :epsilon > 0 there exists : delta>0 such that for any measurable set E, mu(E) …   Wikipedia

• Uniform convergence — In the mathematical field of analysis, uniform convergence is a type of convergence stronger than pointwise convergence. A sequence {fn} of functions converges uniformly to a limiting function f if the speed of convergence of fn(x) to f(x) does… …   Wikipedia

• Uniform continuity — In mathematical analysis, a function f ( x ) is called uniformly continuous if, roughly speaking, small changes in the input x effect small changes in the output f ( x ) ( continuity ), and furthermore the size of the changes in f ( x ) depends… …   Wikipedia

• 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

• List of mathematics articles (U) — NOTOC U U duality U quadratic distribution U statistic UCT Mathematics Competition Ugly duckling theorem Ulam numbers Ulam spiral Ultraconnected space Ultrafilter Ultrafinitism Ultrahyperbolic wave equation Ultralimit Ultrametric space… …   Wikipedia

• Fatou's lemma — In mathematics, Fatou s lemma establishes an inequality relating the integral (in the sense of Lebesgue) of the limit inferior of a sequence of functions to the limit inferior of integrals of these functions. The lemma is named after the French… …   Wikipedia

• Dirichlet kernel — In mathematical analysis, the Dirichlet kernel is the collection of functions It is named after Johann Peter Gustav Lejeune Dirichlet. The importance of the Dirichlet kernel comes from its relation to Fourier series. The convolution of Dn(x) with …   Wikipedia

• Doob's martingale convergence theorems — In mathematics specifically, in stochastic analysis Doob s martingale convergence theorems are a collection of results on the long time limits of supermartingales, named after the American mathematician Joseph Leo Doob. Contents 1 Statement of… …   Wikipedia

• Relatively compact subspace — In mathematics, a relatively compact subspace (or relatively compact subset) Y of a topological space X is a subset whose closure is compact.Since closed subsets of compact spaces are compact, every set in a compact space is relatively compact.… …   Wikipedia

• Continuous function — Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables Implicit differentiation Taylor s theorem Related rates …   Wikipedia