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Question on the difference between a limit of an integral and if a function is integrable

score 682 · Answer 1 · 2026-04-10 07:34:40

682

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Question on the difference between a limit of an integral and if a function is integrable

Published on 10 Apr 2026 - 7:34

score 57 · Answer 2 · 2026-04-14 02:42:13

57

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Reconstructing a measure from its (absolutely continuous) marginals

Published on 14 Apr 2026 - 2:42

score 220 · Answer 3 · 2026-04-14 10:44:10

220

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Any function in $L^p$ space is a linear combination of simple functions? True OR not?

Published on 14 Apr 2026 - 10:44

score 212 · Answer 4 · 2026-04-13 19:54:35

212

Views

Finite meaure space with $f \in L^p$

Published on 13 Apr 2026 - 19:54

score 7.6k · Answer 5 · 2026-04-14 05:33:11

7.6k

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Finite measure space & sigma-finite measure space

Published on 14 Apr 2026 - 5:33

score 885 · Answer 6 · 2026-04-14 21:22:40

885

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I need to prove whether two sequences are equidistributed or not

Published on 14 Apr 2026 - 21:22

score 311 · Answer 7 · 2026-04-16 15:19:17

311

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Let $1 \leq p <\infty$ and $f \in L^p(\mathbb{R})$. Prove $\lim_{x \to \infty} \int_x^{x+1} f(t) dt = 0$.

Published on 16 Apr 2026 - 15:19

score 37 · Answer 8 · 2026-04-14 04:50:01

37

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Is this sufficient for $f'' \in L^2$?

Published on 14 Apr 2026 - 4:50

score 76 · Answer 9 · 2026-04-10 17:49:05

76

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Existence of double integral

Published on 10 Apr 2026 - 17:49

score 405 · Answer 10 · 2026-04-15 06:05:23

405

Views

A Quick Question on the Monotone Property of Integrals.

Published on 15 Apr 2026 - 6:05

score 1.6k · Answer 11 · 2026-04-11 18:46:46

1.6k

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Do Riemann and Lebesgue integrals always agree?

Published on 11 Apr 2026 - 18:46

score 116 · Answer 12 · 2026-04-16 05:55:28

116

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Given $f\in L^1(\mathbb{R})$ with $\|f\|_1<\infty$ and $g_n=\sqrt{n/2\pi}e^{-nx^2/2},f_n=g_n\ast f$, show that $\lim\|f_n-f\|_1=0$

Published on 16 Apr 2026 - 5:55

score 60 · Answer 13 · 2026-04-13 07:53:12

60

Views

Does the integral converge I can't find counterexample

Published on 13 Apr 2026 - 7:53

score 531 · Answer 14 · 2026-04-15 14:49:47

If $\lim_{n\to\infty} \int_E f_n dx$ is finite, prove $f$ is Lebesgue integrable on $E$ and $\lim_{n\to\infty} \int_E f_n dx=\int_E fdx$.

score 4.3k · Answer 15 · 2026-04-12 10:44:50

4.3k

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Why does Fubini's theorem not hold/apply to this function?

Published on 12 Apr 2026 - 10:44

List Question

Question on the difference between a limit of an integral and if a function is integrable

Reconstructing a measure from its (absolutely continuous) marginals

Any function in $L^p$ space is a linear combination of simple functions? True OR not?

Finite meaure space with $f \in L^p$

Finite measure space & sigma-finite measure space

I need to prove whether two sequences are equidistributed or not

Let $1 \leq p <\infty$ and $f \in L^p(\mathbb{R})$. Prove $\lim_{x \to \infty} \int_x^{x+1} f(t) dt = 0$.

Is this sufficient for $f'' \in L^2$?

Existence of double integral

A Quick Question on the Monotone Property of Integrals.

Do Riemann and Lebesgue integrals always agree?

Given $f\in L^1(\mathbb{R})$ with $\|f\|_1<\infty$ and $g_n=\sqrt{n/2\pi}e^{-nx^2/2},f_n=g_n\ast f$, show that $\lim\|f_n-f\|_1=0$

Does the integral converge I can't find counterexample

If $\lim_{n\to\infty} \int_E f_n dx$ is finite, prove $f$ is Lebesgue integrable on $E$ and $\lim_{n\to\infty} \int_E f_n dx=\int_E fdx$.

Why does Fubini's theorem not hold/apply to this function?

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