Corollary

Tag 0AC3, permanent. Cite it as [Bourbaki, Tag 0AC3].

Lie Groups and Lie Algebras, chapter III, § 3. Passage from a Lie group to its Lie algebra

Let $G$ be a finite-dimensional real Lie group, $\mu$ (resp. $\nu$ ) a left (resp. right) Haar measure on $G$ , $k$ an integer $\geqslant 0$ , $u \in U_k(G)$ and $f$ and $g$ real-valued functions of class $C^k$ on $G$ with compact support. Then

\int_G (R_u f) g \, d\mu = \int_G f (R_u^\nu g) \, d\mu

\int_G (L_u f) g \, d\nu = \int_G f (L_u^\nu g) \, d\nu.

This follows from Proposition 57 and \emph{Differentiable and Analytic Manifolds}, R, 14.3.8.

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

Cited by

Nothing.

Cites

Proposition 57