Corollary 1

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

Integration, VIII, p. 43, § 4. Convolution of measures and functions

— Let H be a subgroup of G measurable for a Haar measure $\beta$ . Then H is either open or locally $\beta$ -negligible.

For, $H = H \cdot H^{-1}$ , therefore if H is not locally $\beta$ -negligible, then H contains a neighborhood of e (Prop. 17) hence is open (GT, III, §2, No. 1, Cor. of Prop. 4).

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

Cited by

Corollary 2, § 4

Cites

III, §2, No. 1
Prop. 17