# Choquet’s capacitability theorem

Choquet’s capacitability theorem states that analytic sets (http://planetmath.org/AnalyticSet2) are capacitable.

###### Theorem (Choquet).

Let $\mathcal{F}$ be a paving that is closed under finite unions and finite intersections. If $I$ is an $\mathcal{F}$-capacity, then all $\mathcal{F}$-analytic sets are $(\mathcal{F},I)$-capacitable.

A useful consequence of this result for applicatons to measure theory is the universal measurability of analytic sets (http://planetmath.org/MeasurabilityOfAnalyticSets).

Title Choquet’s capacitability theorem ChoquetsCapacitabilityTheorem 2013-03-22 18:47:49 2013-03-22 18:47:49 gel (22282) gel (22282) 4 gel (22282) Theorem msc 28A05 msc 28A12 capacitability theorem