uniformly continuous and $\int_0^\infty f(t)\,\mathrm dt$ exists $\implies \lim_{x\to\infty}f(x) = 0 $

Asked May 20 '13 at 13:15

Active May 20 '13 at 13:40

Viewed 210 times

I appreciate your help with this one. Let $f \colon[0,\infty)\rightarrow \mathbb{R}$ be uniformly continuous and let the integral $\int_0^\infty f(t)\,\mathrm dt$ exist and be final.

I need to show that $$\lim_{x\to\infty}f(x) = 0. $$

Thank you very much.

edited May 20 '13 at 13:40

Hagen von Eitzen

374,180

asked May 20 '13 at 13:15

Simba

5

See this. – David Mitra May 20 '13 at 13:20
@DavidMitra thank you very much! and im sorry for the duplicate. – Simba May 20 '13 at 18:49

uniformly continuous and $\int_0^\infty f(t)\,\mathrm dt$ exists $\implies \lim_{x\to\infty}f(x) = 0 $

0 Answers0