PlanetMath: Choquet's capacitability theorem

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Choquet's capacitability theorem

(Theorem)

Choquet's capacitability theorem states that analytic sets 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.

"Choquet's capacitability theorem" is owned by gel.

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Other names:

capacitability theorem

Keywords:

capacity, capacitable, analytic set

This object's parent.

Attachments:: proof of Choquet's capacitability theorem (Proof) by gel

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Cross-references: measure, intersections, unions, closed under, paving, capacitable
There are 3 references to this entry.

This is version 1 of Choquet's capacitability theorem, born on 2009-02-02.
Object id is 11596, canonical name is ChoquetsCapacitabilityTheorem.
Accessed 566 times total.

Classification:

AMS MSC:	28A05 (Measure and integration :: Classical measure theory :: Classes of sets , measurable sets, Suslin sets, analytic sets)
	28A12 (Measure and integration :: Classical measure theory :: Contents, measures, outer measures, capacities)

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