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

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