
Accession Number : AD0654476
Title : REPRESENTATION OF NONNEGATIVE CONTINUOUS FUNCTIONS ON PRODUCT SPACES.
Descriptive Note : Technical rept.,
Corporate Author : MICHIGAN STATE UNIV EAST LANSING
Personal Author(s) : Rubin,Herman
Report Date : 12 JUN 1967
Pagination or Media Count : 6
Abstract : The purpose of this note is to show that a nonnegative continuous function on a locally compact sigmacompact product space is a countable sum of products of factor functions. That is, if f is a nonnegative continuous function on Chi(subscript alpha, epsilon, A)X(subscript alpha), there exist nonnegative continuous functions g(subscript alpha i), such that for each i only finitely many g(subscript alpha i) are not identically 1, and for all x, f(x) = Summation over i of (Phi(subscript alpha) g(subscript alpha i)x(subscript alpha)).
Descriptors : (*FUNCTIONS(MATHEMATICS), MATHEMATICS), INEQUALITIES, THEORY
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE