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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.

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marked as duplicate by David Mitra, icurays1, fgp, Did, Martin Sleziak May 20 '13 at 14:40

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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