Question

Radon measure determined by the intersection of half lines in the plane

score 125 · Answer 1 · 2026-04-01 09:02:00

125

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Radon measure determined by the intersection of half lines in the plane

Published on 01 Apr 2026 - 9:02

score 121 · Answer 2 · 2026-04-11 15:10:07

121

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Definition of integral in the context of measure theory

Published on 11 Apr 2026 - 15:10

score 140 · Answer 3 · 2026-04-15 21:17:37

140

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Proving $f$ is $L^1$ implies convergence of $\sum_{k \in \mathbb{Z}}{ 2^k*m(|f| > 2^k)}$

Published on 15 Apr 2026 - 21:17

score 65 · Answer 4 · 2026-04-16 01:50:04

65

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Show that $f$ is summable on $A$ and $\lim_{n\rightarrow \infty} \int_A f_n dm=\int_A f dm$

Published on 16 Apr 2026 - 1:50

score 3.8k · Answer 5 · 2026-04-13 16:03:09

3.8k

Views

Using Lebesgue's dominated convergence theorem to show a function is continuous.

Published on 13 Apr 2026 - 16:03

score 106 · Answer 6 · 2026-04-09 00:33:58

106

Views

Understanding the proof for Lebesgue integrability criterion

Published on 09 Apr 2026 - 0:33

score 80 · Answer 7 · 2026-04-15 12:46:37

80

Views

Use monotone convergence theorem to show that $f(x)=\frac{1}{x}$ is not summable on $(0,1)$

Published on 15 Apr 2026 - 12:46

score 521 · Answer 8 · 2026-04-15 07:37:15

521

Views

Product of $L^{1}$ Function and Exponentially Integrable Function

Published on 15 Apr 2026 - 7:37

score 1.1k · Answer 9 · 2026-03-30 20:45:12

1.1k

Views

Counterexample of the almost-inverse of the Fundamnetal Theorem of Calculus(Lebesgue).

Published on 30 Mar 2026 - 20:45

score 109 · Answer 10 · 2026-04-17 06:21:20

109

Views

evaluating Lebesgue integral 3

Published on 17 Apr 2026 - 6:21

score 412 · Answer 11 · 2026-04-13 00:50:44

412

Views

$\int\limits_{\Omega}{uvdx}<\infty,\forall v\in H_0^1(\Omega)$ implies $u\in L^{6/5}(\Omega)$

Published on 13 Apr 2026 - 0:50

score 295 · Answer 12 · 2026-04-13 16:12:29

295

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Let $f: [0,\infty) \to \mathbb R$ be a $\lambda$-integrable function such that $\int_{[0,t]} f\,d\lambda =0$ for all $t\ge 0$. Prove that $f=0$ a.e.

Published on 13 Apr 2026 - 16:12

score 59 · Answer 13 · 2026-04-13 05:54:42

59

Views

a Very simple example

Published on 13 Apr 2026 - 5:54

score 323 · Answer 14 · 2026-04-12 08:36:44

323

Views

Prove a function vanishes almost everywhere.

Published on 12 Apr 2026 - 8:36

score 655 · Answer 15 · 2026-04-09 16:28:53

655

Views

An integrable function is finite a.e.

Published on 09 Apr 2026 - 16:28

List Question

Radon measure determined by the intersection of half lines in the plane

Definition of integral in the context of measure theory

Proving $f$ is $L^1$ implies convergence of $\sum_{k \in \mathbb{Z}}{ 2^k*m(|f| > 2^k)}$

Show that $f$ is summable on $A$ and $\lim_{n\rightarrow \infty} \int_A f_n dm=\int_A f dm$

Using Lebesgue's dominated convergence theorem to show a function is continuous.

Understanding the proof for Lebesgue integrability criterion

Use monotone convergence theorem to show that $f(x)=\frac{1}{x}$ is not summable on $(0,1)$

Product of $L^{1}$ Function and Exponentially Integrable Function

Counterexample of the almost-inverse of the Fundamnetal Theorem of Calculus(Lebesgue).

evaluating Lebesgue integral 3

$\int\limits_{\Omega}{uvdx}<\infty,\forall v\in H_0^1(\Omega)$ implies $u\in L^{6/5}(\Omega)$

Let $f: [0,\infty) \to \mathbb R$ be a $\lambda$-integrable function such that $\int_{[0,t]} f\,d\lambda =0$ for all $t\ge 0$. Prove that $f=0$ a.e.

a Very simple example

Prove a function vanishes almost everywhere.

An integrable function is finite a.e.

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