Accession Number : AD0654476

Title :   REPRESENTATION OF NON-NEGATIVE 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 non-negative continuous function on a locally compact sigma-compact product space is a countable sum of products of factor functions. That is, if f is a non-negative continuous function on Chi(subscript alpha, epsilon, A)X(subscript alpha), there exist non-negative 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