Proposition 3

Tag 087E, permanent. Cite it as [Bourbaki, Tag 087E].

Functions of a Real Variable, chapter II, § 1. PRIMITIVES AND INTEGRALS

Every continuous vector function on an interval $I \subset \mathbf{R}$ taking its values in a complete normed space $E$ over $\mathbf{R}$ is regulated, and admits a primitive on $I$ , of which it is the derivative at every point.

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

Cited by

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Cites

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