Question

Let $f:[0,1] \to \mathbb{R}$ be given by $f(x)=0$ if $x$ rational and if $x$ is irrational , then $f(x)=9^n$

score 1.6k · Answer 1 · 2026-04-15 19:14:26

1.6k

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Let $f:[0,1] \to \mathbb{R}$ be given by $f(x)=0$ if $x$ rational and if $x$ is irrational , then $f(x)=9^n$

Published on 15 Apr 2026 - 19:14

score 62 · Answer 2 · 2026-04-16 07:39:48

62

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Can anyone please let me know where have I gone wrong in evaluating $\int_{-1}^{1} f(t) \cos^2(nt) dt$

Published on 16 Apr 2026 - 7:39

score 75 · Answer 3 · 2026-04-16 00:26:57

75

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If $\int_{|x| \leq r} |f(x)|dx \leq (r+1)^a$, then $\int_{\mathbb{R}} |f(x)|e^{-|tx|} dx < \infty$ for $t \neq 0$

Published on 16 Apr 2026 - 0:26

score 235 · Answer 4 · 2026-04-15 20:51:38

235

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Show that if $f$ is Lebesgue integrable and $g$ is Lipschitz on $\mathbb R,$ then $g\circ f$ is Lebesgue integrable.

Published on 15 Apr 2026 - 20:51

score 439 · Answer 5 · 2026-04-09 13:48:17

439

Views

Translation function of Lebesgue integral is continuous

Published on 09 Apr 2026 - 13:48

score 70 · Answer 6 · 2026-04-16 09:35:04

70

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Show that: $\lim\limits_{|x|\to \infty}f_r(x)=0$

Published on 16 Apr 2026 - 9:35

score 53 · Answer 7 · 2026-04-16 19:57:11

53

Views

Prove $n \mu(|f| \geq n) \to 0$ for any integrable $f$

Published on 16 Apr 2026 - 19:57

score 104 · Answer 8 · 2026-03-26 07:59:17

104

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Could be this:( $f$ is Lebesgue integral $\iff$ $f$ is Borel-summable ) works?

Published on 26 Mar 2026 - 7:59

score 155 · Answer 9 · 2026-04-11 11:36:49

155

Views

How to define $0\cdot\infty$ in Lebesgue's integral?

Published on 11 Apr 2026 - 11:36

score 51.1k · Answer 10 · 2026-04-09 21:14:39

51.1k

Views

Lebesgue integral basics

Published on 09 Apr 2026 - 21:14

score 334 · Answer 11 · 2026-05-02 10:19:56

334

Views

Convergence of integrals in $L^p$ and $L^{p/(p-1)}$

Published on 02 May 2026 - 10:19

score 19.6k · Answer 12 · 2026-04-16 08:26:43

19.6k

Views

If $\int_0^x f \ dm$ is zero everywhere then $f$ is zero almost everywhere

Published on 16 Apr 2026 - 8:26

score 6k · Answer 13 · 2026-04-23 11:15:05

6k

Views

Why do we restrict the definition of Lebesgue Integrability?

Published on 23 Apr 2026 - 11:15

score 586 · Answer 14 · 2026-05-02 17:28:09

586

Views

Convergence of functions in $L^p$

Published on 02 May 2026 - 17:28

score 145 · Answer 15 · 2026-04-11 09:09:29

145

Views

What is the name of this method in Lebesgue integral

Published on 11 Apr 2026 - 9:09

List Question

Let $f:[0,1] \to \mathbb{R}$ be given by $f(x)=0$ if $x$ rational and if $x$ is irrational , then $f(x)=9^n$

Can anyone please let me know where have I gone wrong in evaluating $\int_{-1}^{1} f(t) \cos^2(nt) dt$

If $\int_{|x| \leq r} |f(x)|dx \leq (r+1)^a$, then $\int_{\mathbb{R}} |f(x)|e^{-|tx|} dx < \infty$ for $t \neq 0$

Show that if $f$ is Lebesgue integrable and $g$ is Lipschitz on $\mathbb R,$ then $g\circ f$ is Lebesgue integrable.

Translation function of Lebesgue integral is continuous

Show that: $\lim\limits_{|x|\to \infty}f_r(x)=0$

Prove $n \mu(|f| \geq n) \to 0$ for any integrable $f$

Could be this:( $f$ is Lebesgue integral $\iff$ $f$ is Borel-summable ) works?

How to define $0\cdot\infty$ in Lebesgue's integral?

Lebesgue integral basics

Convergence of integrals in $L^p$ and $L^{p/(p-1)}$

If $\int_0^x f \ dm$ is zero everywhere then $f$ is zero almost everywhere

Why do we restrict the definition of Lebesgue Integrability?

Convergence of functions in $L^p$

What is the name of this method in Lebesgue integral

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