Choquet’s capacitability theorem

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

Theorem (Choquet).

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

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