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{\displaystyle (X,\Sigma )} is called a measurable space, and the members of Σ {\displaystyle \Sigma } are called measurable sets. A triple ( X , Σ , μ ) {\displaystyle...

and in particular measure theory, a measurable function is a function between the underlying sets of two measurable spaces that preserves the structure...

In mathematics, a non-measurable set is a set which cannot be assigned a meaningful "volume". The existence of such sets is construed to provide information...

In mathematics, a measurable space or Borel space is a basic object in measure theory. It consists of a set and a σ-algebra, which defines the subsets...

be assigned a Lebesgue measure are called Lebesgue-measurable; the measure of the Lebesgue-measurable set A is here denoted by λ(A). Henri Lebesgue described...

Bochner-measurable function taking values in a Banach space is a function that equals almost everywhere the limit of a sequence of measurable countably-valued...

is an elementary example of a set of real numbers that is not Lebesgue measurable, found by Giuseppe Vitali in 1905. The Vitali theorem is the existence...

category of measurable spaces, often denoted Meas, is the category whose objects are measurable spaces and whose morphisms are measurable maps. This is...

In mathematics, a measurable cardinal is a certain kind of large cardinal number. In order to define the concept, one introduces a two-valued measure on...

In mathematics, progressive measurability is a property in the theory of stochastic processes. A progressively measurable process, while defined quite...

where he advocated for setting objectives that are specific (or Simple), measurable, assignable, realistic, and time-bound—hence the acronym S.M.A.R.T. Since...

product sigma-algebra of measurable spaces is defined to be the finest such that the projection mappings will be measurable. Sometimes for some reasons...

every locally measurable set is also measurable. A set E {\displaystyle E} , not necessarily measurable, is said to be a locally measurable set if for every...

{\displaystyle A} of a Polish space X {\displaystyle X} is universally measurable if it is measurable with respect to every complete probability measure on X {\displaystyle...

In mathematics, a measurable group is a special type of group in the intersection between group theory and measure theory. Measurable groups are used to...

that it is not a true measure in its modern definition, since Jordan-measurable sets do not form a σ-algebra. For example, singleton sets { x } x ∈ R...

Strong measurability has a number of different meanings, some of which are explained below. For a function f with values in a Banach space (or Fréchet...

mathematician Constantin Carathéodory that characterizes when a set is Lebesgue measurable. Carathéodory's criterion: Let λ ∗ : P ( R n ) → [ 0 , ∞ ] {\displaystyle...

Sk are disjoint measurable sets, is called a measurable simple function. We extend the integral by linearity to non-negative measurable simple functions...

mathematics, a measurable acting group is a special group that acts on some space in a way that is compatible with structures of measure theory. Measurable acting...