Proposition 5

Tag 08E2, permanent. Cite it as [Bourbaki, Tag 08E2].

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 $\mathscr{H}(\mathfrak{F}, \mathbf{R})$ . Then the relations $f_1 \ll g$ and $f_2 \ll g$ imply $f_1 + f_2 \ll g$ .

Moreover, the same argument as in prop. 3 of V, p. 213 shows that:

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

Cited by

Nothing.

Cites

V, p. 213