countable additivity
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σ-additivity — noun countable additivity … Wiktionary
Measure (mathematics) — Informally, a measure has the property of being monotone in the sense that if A is a subset of B, the measure of A is less than or equal to the measure of B. Furthermore, the measure of the empty set is required to be 0. In mathematical analysis … Wikipedia
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
Non-measurable set — This page gives a general overview of the concept of non measurable sets. For a precise definition of measure, see Measure (mathematics). For various constructions of non measurable sets, see Vitali set, Hausdorff paradox, and Banach–Tarski… … Wikipedia
Probability measure — In some cases, statistical physics uses probability measures, but not all measures it uses are probability measures.[1][2] In mathematics, a probability measure is a real valued function defined on a set … Wikipedia
Vitali set — In mathematics, a Vitali set is an elementary example of a set of real numbers that is not Lebesgue measurable. The Vitali theorem is the existence theorem that there are such sets. It is a non constructive result. The naming is for Giuseppe… … 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
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
Bayesian probability — Bayesian statistics Theory Bayesian probability Probability interpretations Bayes theorem Bayes rule · Bayes factor Bayesian inference Bayesian network Prior · Posterior · Likelihood … Wikipedia
Carathéodory's extension theorem — See also Carathéodory s theorem for other meanings. In measure theory, Carathéodory s extension theorem proves that for a given set Ω, you can always extend a sigma; finite measure defined on R to the sigma; algebra generated by R , where R is a… … Wikipedia
