Question

Limit involving integral $\frac{1}{r}\int_0^r f(s)\, ds \to0$?

score 115 · Answer 1 · 2026-04-15 20:45:20

115

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Limit involving integral $\frac{1}{r}\int_0^r f(s)\, ds \to0$?

Published on 15 Apr 2026 - 20:45

score 48 · Answer 2 · 2026-04-15 14:04:36

48

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Limit of sequence of Lebesgue integrals over symmetric domains

Published on 15 Apr 2026 - 14:04

score 877 · Answer 3 · 2026-04-14 03:46:28

877

Views

Proof of the identity $\int_0^{+\infty}\frac{\sin(x)}{x^\alpha}dx=\frac{\Gamma(\alpha/2)\Gamma(1-\alpha/2)}{2\Gamma(\alpha)}$ for $\alpha\in (0,2)$.

Published on 14 Apr 2026 - 3:46

score 218 · Answer 4 · 2026-04-10 10:11:41

218

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Can I sum over the power set of the natural numbers?

Published on 10 Apr 2026 - 10:11

score 447 · Answer 5 · 2026-04-13 14:55:57

447

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Is this discrete analogue of Fatou's lemma valid

Published on 13 Apr 2026 - 14:55

score 167 · Answer 6 · 2026-04-12 01:08:23

167

Views

Lebesgue integral of non-measurable function which is equal a.e to a measurable function

Published on 12 Apr 2026 - 1:08

score 374 · Answer 7 · 2026-05-05 00:07:12

374

Views

Why $\ln (1/x) \in L^p ( (0, 1] )$ for $1\leq p < \infty$?

Published on 05 May 2026 - 0:07

score 372 · Answer 8 · 2026-04-10 07:42:26

372

Views

change of variable in Lebesgue integration

Published on 10 Apr 2026 - 7:42

score 71 · Answer 9 · 2026-04-12 15:58:13

71

Views

Absolutely convergent doubles sums in Banach spaces

Published on 12 Apr 2026 - 15:58

score 55 · Answer 10 · 2026-04-19 08:18:21

55

Views

$\Gamma: (0,1) \rightarrow \mathbb{R}$, where $\Gamma(\alpha)=\int_{0}^{\infty}e^{-x}x^{\alpha-1}dx $

Published on 19 Apr 2026 - 8:18

score 93 · Answer 11 · 2026-04-15 22:42:13

93

Views

Is it true that $(\int f d \mu)^2 + (\int g d \mu)^2 \leq (\int \sqrt{f^2+g^2} d \mu)^2$

Published on 15 Apr 2026 - 22:42

score 88 · Answer 12 · 2026-04-13 21:04:26

88

Views

Bergman Kernel for $D_R (R>0)$.

Published on 13 Apr 2026 - 21:04

score 133 · Answer 13 · 2026-04-15 20:05:01

133

Views

Prove the infimum of a set of Lebesgue integrals is bigger than 0

Published on 15 Apr 2026 - 20:05

score 140 · Answer 14 · 2026-04-13 12:47:38

140

Views

Does $\int{f_ng_n}$ converge to $\int{fg}$ under certain conditions?

Published on 13 Apr 2026 - 12:47

score 77 · Answer 15 · 2026-04-16 04:22:46

77

Views

$f$ is Lebesgue integrable on $E\subset\mathbb{R}$, what is $I=\{\int_e fdm: \text{Measurable set}\ e\subset E\}$?

Published on 16 Apr 2026 - 4:22

List Question

Limit involving integral $\frac{1}{r}\int_0^r f(s)\, ds \to0$?

Limit of sequence of Lebesgue integrals over symmetric domains

Proof of the identity $\int_0^{+\infty}\frac{\sin(x)}{x^\alpha}dx=\frac{\Gamma(\alpha/2)\Gamma(1-\alpha/2)}{2\Gamma(\alpha)}$ for $\alpha\in (0,2)$.

Can I sum over the power set of the natural numbers?

Is this discrete analogue of Fatou's lemma valid

Lebesgue integral of non-measurable function which is equal a.e to a measurable function

Why $\ln (1/x) \in L^p ( (0, 1] )$ for $1\leq p < \infty$?

change of variable in Lebesgue integration

Absolutely convergent doubles sums in Banach spaces

$\Gamma: (0,1) \rightarrow \mathbb{R}$, where $\Gamma(\alpha)=\int_{0}^{\infty}e^{-x}x^{\alpha-1}dx $

Is it true that $(\int f d \mu)^2 + (\int g d \mu)^2 \leq (\int \sqrt{f^2+g^2} d \mu)^2$

Bergman Kernel for $D_R (R>0)$.

Prove the infimum of a set of Lebesgue integrals is bigger than 0

Does $\int{f_ng_n}$ converge to $\int{fg}$ under certain conditions?

$f$ is Lebesgue integrable on $E\subset\mathbb{R}$, what is $I=\{\int_e fdm: \text{Measurable set}\ e\subset E\}$?

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