Remark 1

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

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

If $f$ is a real regulated function on $I$ , and $g$ is a regulated vector function on an interval containing $f(I)$ , then the composite function $g \circ f$ is not necessarily regulated ( $cf.$ II, p. 79, exerc. 4).

Two particular cases of th. 3 of II, p. 54 are especially important:

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

Cited by

Nothing.

Cites

II, p. 54
II, p. 79