Roman Pol, Piotr Zakrzewski
Published 2019-12-09Version 1
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.
The topology of spaces of probability measures, I
Haar meager sets, their hulls, and relationship to compact sets
On continuity of correspondences of probability measures in the category of Tychonov spaces
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