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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

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What is $\,R([0,1])\,$? – DonAntonio Dec 10 '12 at 4:29
riemann integrable – Miguel Mora Luna Dec 10 '12 at 4:30
Then what's the Riemann-Stieltjes integral to do here? – DonAntonio Dec 10 '12 at 4:31
up vote 1 down vote accepted


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

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I edited my first answer since at first I didn't notice the positiveness requirement – DonAntonio Dec 10 '12 at 4:36

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