Question

Prove that $\limsup_{n \rightarrow \infty} (f_n(x))^{1/n} \leq1 $

score 187 · Answer 1 · 2026-04-24 07:00:02

187

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Prove that $\limsup_{n \rightarrow \infty} (f_n(x))^{1/n} \leq1 $

Published on 24 Apr 2026 - 7:00

score 154 · Answer 2 · 2026-04-14 10:14:38

154

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Convergence of the sum implies convergence of the summands?

Published on 14 Apr 2026 - 10:14

score 1.3k · Answer 3 · 2026-04-10 05:02:49

1.3k

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Boundary of closure of open set in $\mathbb R^2$ has measure zero

Published on 10 Apr 2026 - 5:02

score 1.9k · Answer 4 · 2026-04-24 06:51:23

1.9k

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If $f$ is Lebesgue integrable on $ R$ then $\lim_{h\to 0} \int_R |f(x+h)-f(x)|dx=0? $

Published on 24 Apr 2026 - 6:51

score 977 · Answer 5 · 2026-04-24 08:06:22

977

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Question on Lebesgue point integration

Published on 24 Apr 2026 - 8:06

score 236 · Answer 6 · 2026-04-15 18:57:13

236

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If $y \to f(x,y)$ is Leb-measurable, $x \to f(x,y)$ is continuous, show $f$ is measurable w.r.t. completion of $L \times L$

Published on 15 Apr 2026 - 18:57

score 937 · Answer 7 · 2026-04-24 08:08:59

937

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Show that the Fubini Tonelli theorem does not work for this function

Published on 24 Apr 2026 - 8:08

score 377 · Answer 8 · 2026-04-24 08:13:27

377

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Is this theorem an extension of Scheffé Lemma

Published on 24 Apr 2026 - 8:13

score 73 · Answer 9 · 2026-04-24 08:13:35

73

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Show that the function $g(u)=\int_{-\infty}^{\infty} \frac{x^n e^{ux}}{e^x+1}dx$ is differentiable in $(0,1)$

Published on 24 Apr 2026 - 8:13

score 491 · Answer 10 · 2026-04-11 13:11:41

491

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Proving a set is Lebesgue Measurable

Published on 11 Apr 2026 - 13:11

score 2.5k · Answer 11 · 2026-04-24 08:20:42

2.5k

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Sufficient conditions for the Hardy-Littlewood Maximal function $M(f)$ being continuous

Published on 24 Apr 2026 - 8:20

score 182 · Answer 12 · 2026-04-09 14:10:52

182

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Compact set and measure theory

Published on 09 Apr 2026 - 14:10

score 184 · Answer 13 · 2026-04-15 18:15:05

184

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What is Lebesgue measure of sets of inverse prime numbers in $[0,1] $?

Published on 15 Apr 2026 - 18:15

score 57 · Answer 14 · 2026-04-12 23:36:52

57

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Exponential and convergence in $L^2$

Published on 12 Apr 2026 - 23:36

score 115 · Answer 15 · 2026-04-24 08:14:57

115

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I am seeking a solution using Lebesgue Differentiation Theorem to prove that $|S|=0$, and $|\cdot|$ means Lebesgue measure.

Published on 24 Apr 2026 - 8:14

List Question

Prove that $\limsup_{n \rightarrow \infty} (f_n(x))^{1/n} \leq1 $

Convergence of the sum implies convergence of the summands?

Boundary of closure of open set in $\mathbb R^2$ has measure zero

If $f$ is Lebesgue integrable on $ R$ then $\lim_{h\to 0} \int_R |f(x+h)-f(x)|dx=0? $

Question on Lebesgue point integration

If $y \to f(x,y)$ is Leb-measurable, $x \to f(x,y)$ is continuous, show $f$ is measurable w.r.t. completion of $L \times L$

Show that the Fubini Tonelli theorem does not work for this function

Is this theorem an extension of Scheffé Lemma

Show that the function $g(u)=\int_{-\infty}^{\infty} \frac{x^n e^{ux}}{e^x+1}dx$ is differentiable in $(0,1)$

Proving a set is Lebesgue Measurable

Sufficient conditions for the Hardy-Littlewood Maximal function $M(f)$ being continuous

Compact set and measure theory

What is Lebesgue measure of sets of inverse prime numbers in $[0,1] $?

Exponential and convergence in $L^2$

I am seeking a solution using Lebesgue Differentiation Theorem to prove that $|S|=0$, and $|\cdot|$ means Lebesgue measure.

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