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).

单词	ChoquetsCapacitabilityTheorem
释义	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).
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