Remark 2

Tag 01L8, permanent. Cite it as [Bourbaki, Tag 01L8].

Lie Groups and Lie Algebras, chapter VIII, § 7. Finite dimensional modules over a split semi-simple Lie algebra

By Cor. 1 of Prop. 2 and §5, no. 3, Remark 2, it makes sense to speak of the weights of V with respect to the canonical Cartan subalgebra of $\mathfrak{g}$ , and of their multipicities.

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

§5, no. 3, Remark 2
Cor. 1 of Prop. 2