Bourbaki

Definition 9

Tag 0C9F, permanent. Cite it as [Bourbaki, Tag 0C9F].

General Topology, chapter IX, § 6. Polish spaces, Souslin spaces, Borel sets

Let f be a capacity on X; a subset A of X is said to be capacitable (with respect to f) if f(A)=sup⁡kf(K)f(A) = \sup_k f(K), where K runs through the set of compact subsets of A.

\* For example, if f is an outer measure \mu^*, every open set is capacitable; the capacitable sets A such that \mu^*(A) < +\infty are precisely the \mu-integrable sets. \*

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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Transcribed from the printed volume. Not translated.