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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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