Sign up ×
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.

I'd appreciate it if someone could lead me through the steps for this problem:

Let $f$ be defined and bounded on $[a,b]$. Define a function $g$ on $[a,b]$ by the formula $\overline{I}(\chi_{[a,x]} f)$.

  • Prove $g$ is continuous on $[a,b]$.
  • Suppose $f$ is continuous at $x_0$. Prove that $g'(x_0) = f(x_0)$.
  • Extend to lower integrals.

(In other words $g(x)$ is the upper integral of $f$ on $[a,x]$)

share|cite|improve this question
What is $\bar{I}(\chi_{[a,x]} f)$? – user38268 Nov 21 '11 at 11:54
The upper integral of $f(x)$ on $[a,x]$ – totok Nov 21 '11 at 12:18

Your Answer


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

Browse other questions tagged or ask your own question.