Measures on the product of compact spaces

Abstract

If K is an uncountable metrizable compact space, we prove a ‘factorization’ result for a wide variety of vector valued Borel measures μ defined on Kn. This result essentially says that for every such measure μ there exists a measure μ0 defined on K such that the measure μ of a product A1 ו • •×An of Borel sets of K equals the measure μ0 of the intersection A01 \• • •\A0n, where the A0j’s are certain transforms of the Ai’s.