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On Mazurkiewicz’s sets, thin \(\sigma \)-ideals of compact sets and the space of probability measures on the rationals

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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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Pol, R., Zakrzewski, P. On Mazurkiewicz’s sets, thin \(\sigma \)-ideals of compact sets and the space of probability measures on the rationals. RACSAM 115, 42 (2021). https://doi.org/10.1007/s13398-020-00975-4

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