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Be $E=[0,\infty]$ and $1\leq p\leq \infty$, Exhibit a function $f$ that $f\in \mathcal{L}^p$ and $f\notin \mathcal{L}^q$ when $q \neq p$

I try with simple functions but i dont know if are lebesgue integrable or dont

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    what does "if are leb" mean?2012-07-11
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    I assume at least one of the $p$s should be a $q$.2012-07-11
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    By "simple functions", do you mean the *technical* meaning of simple functions (functions that take only finitely many values, and the inverse image of each value is Lebesgue measurable)? Or do you mean "easy functions", using 'simple' in an informal sense?2012-07-11

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