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 K ⁿ. This result essentially says that for every such measure μ there exists a measure μ′ defined on K such that the measure μ of a product A ₁ × ⋯ × A _n of Borel sets of K equals the measure μ′ of the intersection A ₁′∩⋯∩A _n ′, where the A _i ′’s are certain transforms of the A _i ’s.