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25 Questions

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18	Size of the closure of a set
13	Isometry in compact metric spaces
8	Compute $\lim_{a \to 0^+} \left(a \int_1^{\infty} e^{-ax}\cos \left(\frac{2\pi}{1+x^{2}} \right)\mathrm dx\right)$
7	Convergence of integrals in $L^p$
5	Please explain inequality $\|x^{p}-y^{p}\| \leq \|x-y\|^p$

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392 Reputation

+5	Understanding proof of completeness of $L^{\infty}$
+5	Isometry in compact metric spaces
+5	Convergence of integrals in $L^p$
+5	Doubt inequality almost everywhere

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2 Answers

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1	Compute $\lim_{a \to 0^+} \left(a \int_1^{\infty} e^{-ax}\cos \left(\frac{2\pi}{1+x^{2}} \right)\mathrm dx\right)$
0	Compute integral of a Lebesgue measurable set

11 Tags

1 calculus × 3	0 lp-spaces × 2
1 integral × 2	0 lebesgue-integral
0 measure-theory × 17	0 convergence
0 real-analysis × 3	0 metric-spaces
0 general-topology × 2	0 algebra-precalculus

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