Corollary 1

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

Integration, VII, p. 43, § 2. Quotient of a space by a group; homogeneous spaces

For there to exist on $G/H$ a nonzero positive measure relatively invariant under G, it is necessary and sufficient that there exist a continuous representation of $G$ in $\mathbf{R}_+^*$ extending the representation $\xi \mapsto \Delta_H(\xi)/\Delta_G(\xi)$ .

Note that this condition is fulfilled when $H$ is unimodular.

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

Cited by

Remark, § 3

Cites

Nothing.