Bourbaki

Corollary 2

Tag 09IY, permanent. Cite it as [Bourbaki, Tag 09IY].

Integration, VIII, p. 17, § 2. Linear representations of groups

With hypotheses as in Cor. 1, let ff be a continuous mapping of TT into a quasi-complete locally convex space EE. Then

lim⁡μ,T∫f(t) dμ(t)=f(a). \lim_{\mu,\mathfrak{T}} \int f(t)\, d\mu(t) = f(a).

This follows from Cor. 1, and Prop. 14 of Ch. VI, §1, No. 6.

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.