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A note on the measurability of convex sets. (English) Zbl 0607.28003
The author proves that convex sets in the space \({\mathbb{R}}^ n\) are measurable with respect to every \(\sigma\)-finite product measure on the Borel field \({\mathcal B}^ n\). He shows that the boundary \(\partial A\) of a convex set \(A\subset {\mathbb{R}}^ n\) is negligible with respect to every product measure \(\mu =\otimes_{1\leq i\leq n}\mu_ i\) on the Borel field \({\mathcal B}^ n\) with non-atomic \(\sigma\)-finite marginals \(\mu_ 1,...,\mu_ n.\)
Reviewer: K.Nikodem

MSC:
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
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References:
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