Bourbaki

Remark

Tag 0AC0, permanent. Cite it as [Bourbaki, Tag 0AC0].

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

Preserving the hypotheses and notation of Proposition 52, suppose that KK is locally compact. Let μ\mu be the measure

mod⁡det⁡(Dn+imk(x1,…,xn,x1,…,xn))1≤i,k≤ndx1…dxn \operatorname{mod} \det(D_{n+i}m_k(x_1, \ldots, x_n, x_1, \ldots, x_n))_{1 \leq i, k \leq n} dx_1 \ldots dx_n
on ψ(U)\psi(U). Then ψ−1(μ)\psi^{-1}(\mu) is the restriction to UU of a Haar measure on GG.

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

Cited by

Nothing.

Cites

Transcribed from the printed volume. Not translated.