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topology of measure convergence

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  • Convergence in measure — can refer to two distinct mathematical concepts which both generalize the concept of convergence in probability. Contents 1 Definitions 2 Properties 3 Counterexamples 4 Topology …   Wikipedia

  • Convergence of measures — In mathematics, more specifically measure theory, there are various notions of the convergence of measures. Three of the most common notions of convergence are described below. Contents 1 Total variation convergence of measures 2 Strong… …   Wikipedia

  • Convergence of random variables — In probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to …   Wikipedia

  • Convergence (routing) — This article is about the convergence of topology information in a set of routers. For the transport of voice, video, and data over the same network infrastructure, see Convergence (telecommunications). For other uses, see Convergence.… …   Wikipedia

  • Radon measure — In mathematics (specifically, measure theory), a Radon measure, named after Johann Radon, is a measure on the σ algebra of Borel sets of a Hausdorff topological space X that is locally finite and inner regular. Contents 1 Motivation 2 Definitions …   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

  • Strong operator topology — In functional analysis, a branch of mathematics, the strong operator topology, often abbreviated SOT, is the weakest topology on the set of bounded operators on a Hilbert space (or, more generally, on a Banach space) such that the evaluation map… …   Wikipedia

  • Maximising measure — In mathematics specifically, in ergodic theory a maximising measure is a particular kind of probability measure. Informally, a probability measure μ is a maximising measure for some function f if the integral of f with respect to μ is “as big as… …   Wikipedia

  • Idempotent measure — In mathematics, an idempotent measure on a metric group is a probability measure that equals its convolution with itself; in other words, an idempotent measure is an idempotent element in the topological semigroup of probability measures on the… …   Wikipedia

  • Pointwise convergence — In mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function.[1][2] Contents 1 Definition 2 Properties …   Wikipedia

  • Modes of convergence — In mathematics, there are many senses in which a sequence or a series is said to be convergent. This article describes various modes (senses or species) of convergence in the settings where they are defined. For a list of modes of convergence,… …   Wikipedia

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