Products of completion regular measures

Abstract

Let X = ∏ i ∈ I X i X = {\prod _{i \in I}}{X_i} and Y = ∏ j ∈ J Y j Y = {\prod _{j \in J}}{Y_j} , where all X i , Y j {X_i},{Y_j} are separable metric spaces. Let μ \mu and ν \nu be completion regular Radon probability measures on X X and Y Y respectively. Then μ × ν \mu \times \nu on X × Y X \times Y is completion regular. This solves a problem of J. R. Choksi and D. H. Fremlin.