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A set function mu is finitely additive if, given any finite disjoint collection of sets {E_k}_(k=1)^n on which mu is defined, mu( union _(k=1)^nE_k)=sum_(k=1)^nmu(E_k).

Let (X,A,mu) and (Y,B,nu) be measure spaces. A measurable rectangle is a set of the form A×B for A in A and B in B.

Let S be a collection of subsets of a set X and let mu:S->[0,infty] be a set function. The function mu is called a premeasure provided that mu is finitely additive, countably ...

A set function is a function whose domain is a collection of sets. In many instances in real analysis, a set function is a function which associates an affinely extended real ...

Fisher's exact test is a statistical test used to determine if there are nonrandom associations between two categorical variables. Let there exist two such variables X and Y, ...

The median of a statistical distribution with distribution function D(x) is the value x such D(x)=1/2. For a symmetric distribution, it is therefore equal to the mean. Given ...

Given a complex Hilbert space H with associated space L(H) of continuous linear operators from H to itself, the bicommutant M^('') of an arbitrary subset M subset= L(H) is ...

The bicommutant theorem is a theorem within the field of functional analysis regarding certain topological properties of function algebras. The theorem says that, given a ...

The term Borel hierarchy is used to describe a collection of subsets of R defined inductively as follows: Level one consists of all open and closed subsets of R, and upon ...

Let S be a collection of subsets of a set X, mu:S->[0,infty] a set function, and mu^* the outer measure induced by mu. The measure mu^_ that is the restriction of mu^* to the ...