Remark 2

Tag 01F6, permanent. Cite it as [Bourbaki, Tag 01F6].

Lie Groups and Lie Algebras, chapter IX, § 6. Integration on compact Lie groups

Let $\nu$ be the measure on the quotient $T/W$ defined by

\int_{T/W}\psi (\tau )d\nu (\tau ) =\frac{1}{w(G)}\int_T\psi (\pi (t))\delta_G(t)dt

where $\pi$ denotes the canonical projection of T onto $T/W$ . Cor. 2 means that the homeomorphism $T/W\rightarrow G/$ Int(G) (§2, no. 5, Cor. 1 of Prop. 5) transports the measure $\nu$ to the image of the measure $dg$ under the canonical projection $G\rightarrow G/$ Int(G).

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

§2, no. 5, Cor. 1 of Prop. 5
Cor. 2