Corollary 2

Tag 09M7, permanent. Cite it as [Bourbaki, Tag 09M7].

Integration, chapter VIII, § 5. The space of closed subgroups

Let A be a $\mu$ -integrable subset of G. The restriction of the mapping $\alpha \mapsto \| \mu_\alpha \|$ to the set $N_A$ of normalized Haar measures of the discrete subgroups H of G such that $G = AH$ , is vaguely continuous.

For $a \in A$ and $\alpha \in N_A$ ,

\int \varphi_A(as)\ d\alpha(s) \geq \varphi_A(a) = 1,

and since $\pi_\alpha(A) = Q_\alpha$ , one has $N_A \subset \Gamma^0(\varphi_A)$ , and the corollary therefore follows from Prop. 5.

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

Cited by

Nothing.

Cites

Prop. 5