# 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.

# Descriptors:

# Subject Categories:

- Theoretical Mathematics