Convex sets are null-measurable #
E be a finite dimensional real vector space, let
μ be a Haar measure on
s be a
convex set in
E. Then the frontier of
s has measure zero (see
s is a
Haar measure of the frontier of a convex set is zero.
A convex set in a finite dimensional real vector space is null measurable with respect to an additive Haar measure on this space.