REPRESENTATION OF NON-NEGATIVE CONTINUOUS FUNCTIONS ON PRODUCT SPACES.
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)).
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 12, 1967
- Accession Number
- AD0654476
Entities
People
- Herman Rubin
Organizations
- Michigan State University