Proposition 3

Tag 09I7, permanent. Cite it as [Bourbaki, Tag 09I7].

Integration, chapter VIII, § 1. Convolution

— Let $X_1, \ldots, X_n, Y$ be locally compact spaces, $\varphi$ a continuous mapping of $\prod_{i=1}^n X_i$ into $Y$ . Then the mapping

(\mu, \ldots, \mu_n) \mapsto *_{\varphi} (\mu_i)

\prod_{i=1}^n \mathscr{M}^1(X_i)

into

\mathscr{M}^1(Y)

is a continuous multilinear mapping. This follows from Prop. 2 and what has been said in No. 1.

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

Cited by

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