stephen
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 Dec11 comment How to know a function is in $L^p$. I am not sure to see why we get what we want. We don't know anything about $m(\{x | f(x)^p > t\}$. It seems to me that you have only proven the well-known identity $\int g(x) = \int m(\{x | g(x) > t\}$ for any function $g$. Dec11 revised How to know a function is in $L^p$. added 200 characters in body Dec11 asked How to know a function is in $L^p$. Dec11 accepted On the integrability of some functions Dec11 asked On the integrability of some functions Dec11 comment On an identity about integrals I see. Thank you, I did not realize that! Dec10 comment On an identity about integrals Thanks! The way you put it is really intuitive! Dec10 accepted On an identity about integrals Dec10 awarded Scholar Dec10 accepted On one property of the Lebesgue Measure Dec10 awarded Editor Dec10 revised On one property of the Lebesgue Measure added 16 characters in body Dec10 comment On one property of the Lebesgue Measure @Nate. I am not sure I see how the answers address this question. What do you mean by taking complements? Dec10 comment On one property of the Lebesgue Measure @Jacob. $I$ is an arbitrary measurable subset of $[0,1]$. Dec10 asked On one property of the Lebesgue Measure Dec10 awarded Student Dec10 asked On an identity about integrals