A note on the measurability of convex sets
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 \(\mu_ 1,...,\mu_ n.\)
scientific article; zbMATH DE number 3981473