Remark 1

Tag 01F5, permanent. Cite it as [Bourbaki, Tag 01F5].

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

If we take $\varphi = 1$ in Cor. 3, we obtain

$\int_H$ det(Ad $_{\mathfrak{g}/\mathfrak{h}}(h)-1$ ) $dh=w(G)/w(H)$ (8)

and in particular

\int_T\delta_G(t)dt=w(G) \tag{9}

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

Cor. 3