Lebesgue's criterion

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quasar987
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Main Question or Discussion Point

There's a theorem in my real analysis textbook that says

A function f is Riemann-integrable iff the set of its points of discontinuity is of measure zero.


But take say f(x)=1/x. It is only discontinuous as x=0, but it's not integrable on (-e,e). :grumpy:
 

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i could be wrong but i think that theorem only applies to bounded functions.
 
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This looks like a blatant omission of the word "bounded".
 

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