Proposition 3

Tag 09D9, permanent. Cite it as [Bourbaki, Tag 09D9].

If there exists in G a compact neighborhood V of e invariant under the inner automorphisms, then G is unimodular.

For, let $\mu$ be a left Haar measure on G. For every $s \in G$ ,

\mu(V) = \mu(s^{-1}Vs) = \Delta_G(s)\mu(V) ,

whence $\Delta_G(s) = 1$ since $0 < \mu(V) < +\infty$ .

From this, one deduces immediately:

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

Cited by

Nothing.