Proposition 2

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

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

Let $f_1, f_2$ be two functions in $\mathscr{H}(\mathfrak{F}, V)$ and $g$ a function in $\mathscr{H}(\mathfrak{F}, \mathbf{R})$ . The relations $f_1 \preccurlyeq g$ and $f_2 \preccurlyeq g$ imply $f_1 + f_2 \preccurlyeq g$ .

Further:

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

Cited by

Nothing.

Cites

Nothing.