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):

Report Date:

1967-06-12

Pagination or Media Count:

6.0

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 Chisubscript alpha, epsilon, AXsubscript alpha, there exist non-negative continuous functions gsubscript alpha i, such that for each i only finitely many gsubscript alpha i are not identically 1, and for all x, fx Summation over i of Phisubscript alpha gsubscript alpha ixsubscript alpha.

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE