1
$\begingroup$

Give an example of a positive function f on $[0,1]$ such that $f\in R([0,1])$ but $1/f \notin R([0,1])$ Thanks for your help

  • 0
    Then what's the Riemann-Stieltjes integral to do here?2012-12-10

1 Answers 1

1

$f(x)=\begin{cases}\left(x-\frac{1}{2}\right)^2&x\neq\frac{1}{2}\\8&x=\frac{1}{2}\end{cases}$

The above is Riemann integrable in $\,[0,1]\,$ , but $\,\displaystyle{\frac{1}{f(x)}}\,$ is not (why?)

  • 1
    I edited my first answer since at first I didn't notice the positiveness requirement2012-12-10