# Lebesgue Integration of Measurable Function

Can I ask a homework question here?

Let $f$ be measurable and nonnegative in $\mathbb{R}^n$

Define a radial function $f^*(|x|)=\inf\{t:\lambda(\{x:f(x)>t\})\leq|x|\}$.

Show that $\lambda(\{x:f(x)>t\})=\lambda(\{x:f^*(|x|)>t\})$

and conclude that $||f||_p = ||f^*||_p$.

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Can I ask a homework question here? Well, it would be okay if you thought a little bit on your own and showed your efforts or partial results. Try to adapt the answers you got here yesterday... –  t.b. Aug 14 '12 at 13:31
...and please read this: meta.math.stackexchange.com/q/1803/5363. –  t.b. Aug 14 '12 at 13:38
O.K I see. Thank you for your comment. –  Choi Aug 14 '12 at 13:57
Where are you stuck? And I think you should write $f^*(|x|):=\inf\{t:\lambda(\{\color{red}{y}:f(\color{red}y)>t\})\leq |x|\}$, as $x$ is already used. –  Davide Giraudo Aug 14 '12 at 14:47
If Park = Choi, why the multiple accounts? –  Did Aug 15 '12 at 9:25