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Let X be a set and S a collection of subsets of X. A set function mu:S->[0,infty] is said to possess finite monotonicity provided that, whenever a set E in S is covered by a ...

A set function mu is said to possess finite subadditivity if, given any finite disjoint collection of sets {E_k}_(k=1)^n on which mu is defined, mu( union ...

A synonym for analytic function, regular function, differentiable function, complex differentiable function, and holomorphic map (Krantz 1999, p. 16). The word derives from ...

In the field of functional analysis, the Krein-Milman theorem is a result which characterizes all (nonempty) compact convex subsets K of "sufficiently nice" topological ...

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♯. Then A is a left Hilbert algebra if A has an inner product <·,·> satisfying: 1. ...

A topology tau on a topological vector space X=(X,tau) (with X usually assumed to be T2) is said to be locally convex if tau admits a local base at 0 consisting of balanced, ...

Let X be a locally convex topological vector space and let K be a compact subset of X. In functional analysis, Milman's theorem is a result which says that if the closed ...

Let T be a linear operator on a separable Hilbert space. The spectrum sigma(T) of T is the set of lambda such that (T-lambdaI) is not invertible on all of the Hilbert space, ...

There are at least two integrals called the Poisson integral. The first is also known as Bessel's second integral, ...

A subset B of a vector space E is said to be absorbing if for any x in E, there exists a scalar lambda>0 such that x in muB for all mu in F with |mu|>=lambda, where F is the ...