A remark on A+B and A-A for compact sets in R^n

preprint2016arXivOpen access

Abstract

We prove in particular that if A be a compact convex subset of R^n, and B from R^n be an arbitrary compact set then μ(A-A) \ll μ(A+B)^2 / (\sqrt{n} μ(A)), provided that μ(B)\ge μ(A).

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