Corollary

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

Integration, VIII, p. 21, § 3. Convolution of measures on groups

Let G be a locally compact group, $\mu_1, \ldots, \mu_n$ measures on G. For the sequence $(\mu_i)_{1 \leq i \leq n}$ to be convolvable, it is necessary and sufficient that the sequence $(\check{\mu}_{n-i})_{0 \leq i \leq n-1}$ be so, in which case

(\mu_1 * \cdots * \mu_n)^{\vee} = \check{\mu}_n * \cdots * \check{\mu}_1.

This follows from Prop. 7 on considering the isomorphism $x \mapsto x^{-1}$ of G onto the opposite group.

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

Cited by

Nothing.

Cites

Prop. 7