Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

let $E$ subset of $\mathbb R$ be compact and the function $f$ is continuous on $E$ and the function $g$ is integrable on $E$. prove that the function $fg$ is integrable.

share|improve this question
1. You could start accepting some answers. See here how it is done 2. Please read this thread on how to ask homework questions. 3. Note that $f$ is bounded. –  t.b. Oct 31 '11 at 14:43

1 Answer 1

A continuous function $f$ on a compact set $E$ of $\mathbf R$ is bounded; that is, the sup-norm of $f$ is finite (i.e., $\|f\|_\infty < \infty$).

Now note that

$$\int |fg| \leqslant \|f\|_\infty \int |g| < \infty.$$

Also, follow t.b.'s advice please.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.