Choquet capacity

Summary

A Choquet capacity is a monotone set function defined on all subsets of a space. It is continuous along increasing sequences of sets and along decreasing sequences of compact sets. Choquet introduced the notion to treat Newtonian capacity and outer measures in one framework. Its main result, Choquet's capacitability theorem, says that analytic sets can be approximated from inside by compact sets for every Choquet capacity. This theorem is a basic tool for measurability questions in probability and descriptive set theory.