Question

Translating an integrable function creates a sequence that converges to $0$ almost everywhere

score 276 · Answer 1 · 2026-04-29 02:27:20

276

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Translating an integrable function creates a sequence that converges to $0$ almost everywhere

Published on 29 Apr 2026 - 2:27

score 405 · Answer 2 · 2026-04-17 05:02:50

405

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If $0\leq f_n$ and $f_n\rightarrow f$ a.e and $\lim\int_Xf_n=\int_X f$, is it true that $\lim\int_Ef_n=\int_E f$ for all $E\in\mathcal{M}$.

Published on 17 Apr 2026 - 5:02

score 1.3k · Answer 3 · 2026-04-24 06:50:03

1.3k

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Is the limit of an uniformly convergent sequence of integrable functions (with convergent integrands) integrable?

Published on 24 Apr 2026 - 6:50

score 1.2k · Answer 4 · 2026-04-10 18:12:15

1.2k

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Integration, Lebesgue and counting measure

Published on 10 Apr 2026 - 18:12

score 333 · Answer 5 · 2026-04-10 19:05:19

333

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Invariance of integral

Published on 10 Apr 2026 - 19:05

score 79 · Answer 6 · 2026-04-16 17:15:47

Prove that the lebesgue integrals $\lim_{n\to \infty} \int_{[0,1]^n} \frac{x_1^2+ \dots +x_n^2}{x_1+ \dots +x_n} \ d \mathrm{m}(\mathbf{x})=2/3$

score 419 · Answer 7 · 2026-04-15 07:14:40

419

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How to prove $\int_0^\infty e^{-x}\frac{\sin^2 x}{x}\text{ dx}=\frac{\text{log }5}{4}$

Published on 15 Apr 2026 - 7:14

score 474 · Answer 8 · 2026-04-17 23:54:03

474

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How do we prove $\int_I\int_x^1\frac{1}{t}f(t)\text{ dt}\text{ dx}=\int_If(x)\text{ dx}$

Published on 17 Apr 2026 - 23:54

score 1.7k · Answer 9 · 2026-04-15 08:00:25

1.7k

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Hardy-Littlewood maximal function weak type estimate

Published on 15 Apr 2026 - 8:00

score 116 · Answer 10 · 2026-04-26 12:33:55

116

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Understanding this inner product

Published on 26 Apr 2026 - 12:33

score 65 · Answer 11 · 2026-04-15 18:57:50

65

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Bounded $L^p$ functions

Published on 15 Apr 2026 - 18:57

score 2.2k · Answer 12 · 2026-04-14 13:54:44

2.2k

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Function 1/x is not locally integrable

Published on 14 Apr 2026 - 13:54

score 168 · Answer 13 · 2026-04-10 22:05:05

168

Views

Bounding a maximal function (Estimating an integral)

Published on 10 Apr 2026 - 22:05

score 51 · Answer 14 · 2026-04-14 21:02:56

51

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Better proof for: if $u_n \to u$ in $L^2$ then $F(u_n) \to F(u)$

Published on 14 Apr 2026 - 21:02

score 151 · Answer 15 · 2026-04-12 18:29:20

151

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Some questions on the proof of Hoelders inequality.

Published on 12 Apr 2026 - 18:29

List Question

Translating an integrable function creates a sequence that converges to $0$ almost everywhere

If $0\leq f_n$ and $f_n\rightarrow f$ a.e and $\lim\int_Xf_n=\int_X f$, is it true that $\lim\int_Ef_n=\int_E f$ for all $E\in\mathcal{M}$.

Is the limit of an uniformly convergent sequence of integrable functions (with convergent integrands) integrable?

Integration, Lebesgue and counting measure

Invariance of integral

Prove that the lebesgue integrals $\lim_{n\to \infty} \int_{[0,1]^n} \frac{x_1^2+ \dots +x_n^2}{x_1+ \dots +x_n} \ d \mathrm{m}(\mathbf{x})=2/3$

How to prove $\int_0^\infty e^{-x}\frac{\sin^2 x}{x}\text{ dx}=\frac{\text{log }5}{4}$

How do we prove $\int_I\int_x^1\frac{1}{t}f(t)\text{ dt}\text{ dx}=\int_If(x)\text{ dx}$

Hardy-Littlewood maximal function weak type estimate

Understanding this inner product

Bounded $L^p$ functions

Function 1/x is not locally integrable

Bounding a maximal function (Estimating an integral)

Better proof for: if $u_n \to u$ in $L^2$ then $F(u_n) \to F(u)$

Some questions on the proof of Hoelders inequality.

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