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Convex sets are null-measurable #

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Let E be a finite dimensional real vector space, let μ be a Haar measure on E, let s be a convex set in E. Then the frontier of s has measure zero (see convex.add_haar_frontier), hence s is a measure_theory.null_measurable_set (see convex.null_measurable_set).

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.