REPRESENTATION OF NON-NEGATIVE CONTINUOUS FUNCTIONS ON PRODUCT SPACES.
MICHIGAN STATE UNIV EAST LANSING
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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.
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