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We shall establish some properties of thin $\sigma$-ideals of compact sets incompact metric spaces (in particular, the $\sigma$-ideals of compact null-setsfor thin subadditive capacities), and we shall refine the celebrated theorem ofDavid Preiss that there exist compact non-uniformly tight sets of probabilitymeasures on the rationals.  Both topics will be based on a construction of Stefan Mazurkiewicz from his1927 paper containing a solution of a Urysohn's problem in dimension theory.

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