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Random symmetrizations of measurable sets

2009/02/03 by Aljoša Volčič, Aljosa Volcic, Volcic, Aljosa
Mathematics · #60D05 (Primary) 52A40 (Secondary) #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #Probability (math.PR) #math.FA #math.PR #msc:52A40 #msc:60D05

paper · pdf · doi:10.48550/arxiv.0902.0462

15 pages, submitted

arxiv created 2009/02/03 · openalex publication_date 2009/02/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove almost sure convergence to the ball, in the Nikodym metric, of sequences of random Steiner symmetrizations of bounded Caccioppoli and bounded measurable sets, paralleling a result due to Mani-Levitska concerning convex bodies.

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