Question

Why is it enough to consider simple functions on open intervals to prove the Riemann-Lebesgue lemma?

score 97 · Answer 1 · 2018-11-01 19:31:25

97

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Why is it enough to consider simple functions on open intervals to prove the Riemann-Lebesgue lemma?

Published on 01 Nov 2018 - 19:31

score 45 · Answer 2 · 2026-03-26 16:07:10

45

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$t \in \mathbb{R}$ s.t. $f(t)=\int_{0}^{+\infty}\sin(x^t) \ dx, t\in\mathbb{R}$ exists

Published on 26 Mar 2026 - 16:07

score 171 · Answer 3 · 2018-11-02 19:02:02

171

Views

The Lebesgue integral of nonnegative function

Published on 02 Nov 2018 - 19:02

score 34 · Answer 4 · 2026-03-25 07:47:42

34

Views

About a Lebesgue intergrability condition

Published on 25 Mar 2026 - 7:47

score 80 · Answer 5 · 2018-11-04 16:50:03

80

Views

Limit in $L^{1}(\mathbb{R})$

Published on 04 Nov 2018 - 16:50

score 332 · Answer 6 · 2018-11-04 17:41:19

332

Views

Given Limit is the Essential Supremum

Published on 04 Nov 2018 - 17:41

score 71 · Answer 7 · 2018-11-04 21:39:23

71

Views

Sum of Integrals and $L^{p}$ Spaces

Published on 04 Nov 2018 - 21:39

score 670 · Answer 8 · 2026-03-25 06:06:17

670

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$f:[0,1] \to \mathbb R$ be a differentiable function with bounded derivative, then is $\int_0^1 f'(x)=f(1)-f(0)$?

Published on 25 Mar 2026 - 6:06

score 68 · Answer 9 · 2018-11-04 23:33:42

68

Views

Is the Norm of the $L^{2}$ Function Equal to the Given Limit?

Published on 04 Nov 2018 - 23:33

score 247 · Answer 10 · 2018-11-05 11:29:33

247

Views

For wich $\alpha > 0$ and $\beta \in \mathbb{R}$ is $f: (1,\infty)\to \mathbb{R}: f(x)=\frac{(\ln(x))^\alpha}{(x-1)^\beta}$ Lebesgue integrable?

Published on 05 Nov 2018 - 11:29

score 396 · Answer 11 · 2018-11-05 17:35:44

396

Views

Prove that the measure of the image of G-delta set, $m(f(G))$, is the integral of the derivative, $\int_{G}f^{'} dm$

Published on 05 Nov 2018 - 17:35

score 81 · Answer 12 · 2018-11-05 17:58:27

81

Views

Lebesgue integrability of $\frac{f(x)}{x}$

Published on 05 Nov 2018 - 17:58

score 89 · Answer 13 · 2018-11-05 23:31:12

89

Views

Is there a notion of an almost measurable function?

Published on 05 Nov 2018 - 23:31

score 148 · Answer 14 · 2018-11-07 00:55:29

148

Views

formula for the integral of characteristic functions of measurable sets

Published on 07 Nov 2018 - 0:55

score 57 · Answer 15 · 2018-11-07 01:13:29

57

Views

Show that $\int_0^\infty \frac{\sin(xt)}{e^t-1}dt = \sum_{n=1}^\infty \frac{x}{n^2+x^2}$

Published on 07 Nov 2018 - 1:13

List Question

Why is it enough to consider simple functions on open intervals to prove the Riemann-Lebesgue lemma?

$t \in \mathbb{R}$ s.t. $f(t)=\int_{0}^{+\infty}\sin(x^t) \ dx, t\in\mathbb{R}$ exists

The Lebesgue integral of nonnegative function

About a Lebesgue intergrability condition

Limit in $L^{1}(\mathbb{R})$

Given Limit is the Essential Supremum

Sum of Integrals and $L^{p}$ Spaces

$f:[0,1] \to \mathbb R$ be a differentiable function with bounded derivative, then is $\int_0^1 f'(x)=f(1)-f(0)$?

Is the Norm of the $L^{2}$ Function Equal to the Given Limit?

For wich $\alpha > 0$ and $\beta \in \mathbb{R}$ is $f: (1,\infty)\to \mathbb{R}: f(x)=\frac{(\ln(x))^\alpha}{(x-1)^\beta}$ Lebesgue integrable?

Prove that the measure of the image of G-delta set, $m(f(G))$, is the integral of the derivative, $\int_{G}f^{'} dm$

Lebesgue integrability of $\frac{f(x)}{x}$

Is there a notion of an almost measurable function?

formula for the integral of characteristic functions of measurable sets

Show that $\int_0^\infty \frac{\sin(xt)}{e^t-1}dt = \sum_{n=1}^\infty \frac{x}{n^2+x^2}$

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