Corollary

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

Integration, VIII, p. 33, § 4. Convolution of measures and functions

Under the hypotheses of Prop. 6, the mapping $(\mu, f) \mapsto \mu *^\beta f$ defines on $L^p(X, \beta)$ the structure of a left module over $\mathscr{M}^{\rho^{1/q}}(G)$ $(1 \leq p \leq +\infty)$ .

This follows from Props. 5 and 6 and the associativity of the convolution product.

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

Cited by

Nothing.

Cites

Prop. 6