Remark 2

Tag 08BS, permanent. Cite it as [Bourbaki, Tag 08BS].

Functions of a Real Variable, chapter IV, § 1. EXISTENCE THEOREMS

When E is of finite dimension, and $\mathbf{f}$ is Lipschitz on $I \times H$ , one can show the existence of approximate solutions of (1) (IV, p. 166, prop. 3) without using the axiom of choice (IV, p. 199, exerc. 1 b)).

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

Cited by

Nothing.

Cites

IV, p. 166
IV, p. 199