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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

##### MSC:
 28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
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##### References:
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