On Mazurkiewicz's sets, thin σ-ideals of compact sets and the space of probability measures on the rationals

2019/12/09 by Roman Pol, Pol, Roman, Piotr Zakrzewski +1
Mathematics · #03E15 #28A12 #28A33 #54H05 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN)

paper · pdf · doi:10.48550/arxiv.1912.04214

openalex publication_date 2019/12/09 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We shall establish some properties of thin σ-ideals of compact sets in compact metric spaces (in particular, the σ-ideals of compact null-sets for thin subadditive capacities), and we shall refine the celebrated theorem of David Preiss that there exist compact non-uniformly tight sets of probability measures on the rationals. Both topics will be based on a construction of Stefan Mazurkiewicz from his 1927 paper containing a solution of a Urysohn's problem in dimension theory.

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