 measurable set

A subset of a given measurable space which is a member of the σalgebra of that space.
Wikipedia foundation.
Wikipedia foundation.
Nonmeasurable 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
Universally measurable set — In mathematics, a subset A of a Polish space X is universally measurable if it is measurable with respect to every complete probability measure on X that measures all Borel subsets of X. In particular, a universally measurable set of reals is… … 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
measurable function — noun a) Any well behaved function of real numbers between measurable spaces. b) If a functions codomain is a topological space and the functions domain is a measurable space, then the function is measurable if the inv … Wiktionary
measurable — UK US /ˈmeʒərəbl/ adjective ► able to be measured: »It is important to set achievable but measurable goals for employees. measurable in sth »He has a fortune measurable in tens of millions. ► large enough to be noticed: »Tax incentives have had a … Financial and business terms
Measurable cardinal — In mathematics, a measurable cardinal is a certain kind of large cardinal number. Contents 1 Measurable 2 Real valued measurable 3 See also 4 References … Wikipedia
Set theory — This article is about the branch of mathematics. For musical set theory, see Set theory (music). A Venn diagram illustrating the intersection of two sets. Set theory is the branch of mathematics that studies sets, which are collections of objects … Wikipedia
measurable space — noun A set with a σ algebra defined on it … Wiktionary
Null set — In mathematics, a null set is a set that is negligible in some sense. For different applications, the meaning of negligible varies. In measure theory, any set of measure 0 is called a null set (or simply a measure zero set). More generally,… … 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