On Mazurkiewicz's sets, thin {\sigma}-ideals of compact sets and the space of probability measures on the rationals

Roman Pol; Piotr Zakrzewski

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arXiv · 1912.04214

On Mazurkiewicz's sets, thin {\sigma}-ideals of compact sets and the space of probability measures on the rationals

Roman Pol·Piotr Zakrzewski

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Abstract

We shall establish some properties of thin $\sigma$-ideals of compact sets in compact metric spaces (in particular, the $\sigma$-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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BibTeX RIS

Roman Pol, Piotr Zakrzewski. 2019-12-09. On Mazurkiewicz's sets, thin {\sigma}-ideals of compact sets and the space of probability measures on the rationals. https://arxiv.org/abs/1912.04214

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