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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 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...

{S}}} , then it is called a measurable group action. In this case, the group G {\displaystyle G} is said to act measurably on S {\displaystyle S} . One...

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

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...

{\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...

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

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...

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...

{\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...

weakly measurable function taking values in a Banach space is a function whose composition with any element of the dual space is a measurable function...

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

Review', where he advocated for setting objectives that are Specific, Measurable, Assignable, Realistic, and Time-bound—hence the acronym S.M.A.R.T. Since...

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...

In economics, a commodity is an economic good, usually a resource, that specifically has full or substantial fungibility: that is, the market treats instances...

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...

of sunshine throughout the year, with an average of only 35 days with measurable precipitation annually. Temperatures in the coastal basin exceed 90 °F...

measurable selection theorem is a result from measure theory that gives a sufficient condition for a set-valued function to have a measurable selection...