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Products of completion regular measures. (English) Zbl 0655.28005
A Radon measure \(\mu\) on a completely regular topological space X is said to be completion regular iff for every Borel set \(E\subset X\) there exist Baire sets \(A,B\subset X\) such that \(A\subset E\subset B\) and \(\mu (B\setminus A)=0.\) The following theorem presented by the author solves a problem posed by J. R. Choksi and D. H. Fremlin: If \(\mu\) and \(\nu\) are completion regular Radon probability measures defined on the products of families of separable metric spaces then the product measure \(\mu \times \nu\) is completion regular. The main tool of the proof is a result giving a characterization of completion regularity of measures on uncountable products of separable metric spaces in terms of the so called elementary open sets.
Reviewer: W.Jarczyk

28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
Full Text: DOI
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