Proposition 4

Tag 08E1, permanent. Cite it as [Bourbaki, Tag 08E1].

Functions of a Real Variable, chapter V, § 1. COMPARISON OF FUNCTIONS ON A FILTERED SET

If $f, g, h$ are three functions in $\mathscr{H}(\mathfrak{F}, \mathbf{R})$ then the relations $f \preccurlyeq g$ and $g \ll h$ (resp. $f \ll g$ and $g \preccurlyeq h$ ) imply $f \ll h$ .

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

Cited by

Proposition 6, § 1

Cites

Nothing.