Corollary 1

Tag 08F5, permanent. Cite it as [Bourbaki, Tag 08F5].

Functions of a Real Variable, chapter V, § 3. ASYMPTOTIC EXPANSIONS OF FUNCTIONS OF A REAL VARIABLE

If $f$ and $g$ are regulated functions and $\geqslant 0$ on the interval $[a, +\infty[$ , and such that $f \succcurlyeq g$ , and if $\int_a^{+\infty} g(t)\,dt = +\infty$ , then $\int_a^{+\infty} f(t)\,dt = +\infty$ .

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

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