The Steinhaus property and Haar-null sets

2009/03/11 by Pandelis Dodos · 1 citation
Computer Science · Mathematics · #Advanced Topology and Set Theory #Digital Image Processing Techniques #Mathematical Dynamics and Fractals #math.FA

paper · pdf · doi:10.1112/blms/bdp014

published as Bulletin of the London Mathematical Society 41 (2009), 377-384 · 9 pages, no figures

openalex publication_date 2009/03/11 · arxiv created 2010/06/14 · arxiv updated 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that, if G is an uncountable Polish group and A ⊆ G is a universally measurable set such that A−1A is meager, then the set Tl(A) = μ ∈ P(G): μ(gA) = 0 for all g ∈ G is co-meager. In particular, if A is analytic and not left Haar-null, then 1 ∈ Int (A−1AA−1A).

Citations

• Classical Descriptive Set Theory

Cited by

• Null set [wikipedia]

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