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.

中文翻译：

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在 Mazurkiewicz 的集合上，紧集的薄 $$\sigma $$-理想和有理数的概率测度空间

我们将在紧度量空间中建立紧集的细$\sigma$-理想的一些性质（特别是对于细次可加容量的紧零集的$\sigma$-理想），我们将改进著名的定理David Preiss 认为在有理数上存在紧凑的非均匀紧概率测度集。这两个主题都将基于 Stefan Mazurkiewicz 在 1927 年发表的论文中的构造，该论文包含维数理论中 Urysohn 问题的解决方案。