Corollary 2

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

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

Let F be a Banach space, $f\in \mathscr{C}^r(X; F)$ ; put

f^{\sharp}(x) =\int_Hf(hx)dh

for $x\in X$ . The function $f^{\sharp}$ is of class $C^r$ , and $f^{\sharp}(hx) =f^{\sharp}(x)$ for $x\in X$ , $h\in H$ .

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

Corollary 3, § 9

Cites

Nothing.