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Results tagged with measure-theory
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user 83274
Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
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Differentiate an integral (Lebesgue integral)
Let $f:[0,1]\to\mathbb{R}$ be a bounded (Lebesgue) measurable function.
Consider the function $$w(p)=\int_0^1|f|^p\,d\mu$$.
Is $w(p)$ differentiable at any $0<p<\infty$? I.e. does $w'(p)$ exist for …
- 1,229