A note on the measurability of convex sets
type: Item
instance of: scholarly article
title: A note on the measurability of convex sets
zbMATH Open document ID: 0607.28003
DOI: 10.1007/BF01202504
author: B. George
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: 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 \(\mu_ 1,...,\mu_ n.\)
Mathematics Subject Classification ID: 28A05
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 3981473
zbMATH Keywords: measurability
zbMATH Keywords: convex sets
zbMATH Keywords: \(\sigma \)-finite product measure
zbMATH Keywords: Borel field
reviewed by: Kazimierz Nikodem
MaRDI profile type: Publication
cites work: On the Embedding of C1(Ω¯) in C0,α(Ω¯)
cites work: Differentiation of integrals in \(\mathbb{R}^n\)
description: scientific article; zbMATH DE number 3981473