A central limit theorem for convex sets

Abstract

Abstract. We show that there exists a sequence εn ց 0 for which the following holds: Let K ⊂ Rn be a compact, convex set with a non-empty interior. Let X be a random vector that is distributed uniformly in K. Then there exist a unit vector θ in Rn, t0 ∈ R and σ> 0 such that sup A⊂R