Proposition 4

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

Integration, VIII, p. 20, § 3. Convolution of measures on groups

The mapping $(\lambda, \mu) \mapsto \lambda * \mu$ (resp. $(\lambda, \mu) \mapsto \mu * \lambda$ ), where $\lambda \in \mathscr{C}'(G)$ , $\mu \in \mathscr{M}(G)$ , defines on $\mathscr{M}(G)$ the structure of a left (resp. right) module over the algebra $\mathscr{C}'(G)$ .

This follows from Props. 1 and 3.

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

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Cites

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