Question

A question about lebesgue integration

score 83 · Answer 1 · 2026-04-09 23:28:38

83

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A question about lebesgue integration

Published on 09 Apr 2026 - 23:28

score 165 · Answer 2 · 2026-04-14 13:30:18

165

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If $u\in H_0^1(\Omega)$ satisfies $-\Delta u=f$, with $f\in C^{\alpha}(\bar{\Omega})$, then $u\in C^{2,\alpha}(\bar{\Omega})$.

Published on 14 Apr 2026 - 13:30

score 1.1k · Answer 3 · 2026-04-15 06:08:30

1.1k

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Why $e^{-x^2}$ is Lebesgue integrable over $\mathbb R$?

Published on 15 Apr 2026 - 6:08

score 57 · Answer 4 · 2026-04-14 17:45:47

57

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Does $x \ f(x) \in L^1(\mathbb{R})$ (lebesgue integrable) imply $f(x)$ is in $L^1(\mathbb{R})$

Published on 14 Apr 2026 - 17:45

score 16.7k · Answer 5 · 2026-04-15 09:30:51

16.7k

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Functions that are Riemann integrable but not Lebesgue integrable

Published on 15 Apr 2026 - 9:30

score 77 · Answer 6 · 2026-04-13 10:26:58

77

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Are These Two Lebesgue Integrals Different?

Published on 13 Apr 2026 - 10:26

score 228 · Answer 7 · 2026-04-17 08:52:33

228

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Calculate $\lim_{n\to\infty}\int_{[0,\infty)}\frac{n\sin\frac{x}{n}}{x(1+x^2)}dx$.

Published on 17 Apr 2026 - 8:52

score 36 · Answer 8 · 2026-04-16 07:27:48

36

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If $|\left \{t\in \mathbb{R}:tv\in A\right \}|=0$ for every $||v||=1$ then $|A|=0$

Published on 16 Apr 2026 - 7:27

score 67 · Answer 9 · 2026-03-27 00:05:07

67

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Help with the Plancherel measure and the norm, on $\mathbb{T}$ and $C_0 (\mathbb{T}) \cap L^1 (\mathbb{T})\}$ respectively.

Published on 27 Mar 2026 - 0:05

score 128 · Answer 10 · 2026-03-26 06:21:14

128

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If a function, $\phi (x)$, has compact support and is in $L^2(\mathbb R)$, then is $x\phi (x) \in L^1(\mathbb R)$?

Published on 26 Mar 2026 - 6:21

score 178 · Answer 11 · 2026-04-29 11:54:13

178

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If $0<|E|<\infty$, $0<||f||_{\infty}<\infty$ and $a_k=||f||_k^k$ then $a_{k+1}/a_k\to ||f||_{\infty}$

Published on 29 Apr 2026 - 11:54

score 56 · Answer 12 · 2026-04-16 21:54:55

56

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$P, Q$ probability measures. Show $P(B) \le P(A_c) \Rightarrow Q(B) \le Q(A_c) \: \: \: \: \forall B \in \mathcal A$ with Lebesgue decomposition.

Published on 16 Apr 2026 - 21:54

score 377 · Answer 13 · 2026-04-29 11:52:40

377

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Proof that $C_{0} ^{\infty}$ bounded functions are dense in $L^{1} (\mathbb{R})$

Published on 29 Apr 2026 - 11:52

score 709 · Answer 14 · 2026-03-28 08:28:05

709

Views

Classical derivative of convolution via weak derivative.

Published on 28 Mar 2026 - 8:28

score 298 · Answer 15 · 2026-04-29 11:54:14

298

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Problem 15.10 of Real analysis for graduate students by R. Bass

Published on 29 Apr 2026 - 11:54

List Question

A question about lebesgue integration

If $u\in H_0^1(\Omega)$ satisfies $-\Delta u=f$, with $f\in C^{\alpha}(\bar{\Omega})$, then $u\in C^{2,\alpha}(\bar{\Omega})$.

Why $e^{-x^2}$ is Lebesgue integrable over $\mathbb R$?

Does $x \ f(x) \in L^1(\mathbb{R})$ (lebesgue integrable) imply $f(x)$ is in $L^1(\mathbb{R})$

Functions that are Riemann integrable but not Lebesgue integrable

Are These Two Lebesgue Integrals Different?

Calculate $\lim_{n\to\infty}\int_{[0,\infty)}\frac{n\sin\frac{x}{n}}{x(1+x^2)}dx$.

If $|\left \{t\in \mathbb{R}:tv\in A\right \}|=0$ for every $||v||=1$ then $|A|=0$

Help with the Plancherel measure and the norm, on $\mathbb{T}$ and $C_0 (\mathbb{T}) \cap L^1 (\mathbb{T})\}$ respectively.

If a function, $\phi (x)$, has compact support and is in $L^2(\mathbb R)$, then is $x\phi (x) \in L^1(\mathbb R)$?

If $0<|E|<\infty$, $0<||f||_{\infty}<\infty$ and $a_k=||f||_k^k$ then $a_{k+1}/a_k\to ||f||_{\infty}$

$P, Q$ probability measures. Show $P(B) \le P(A_c) \Rightarrow Q(B) \le Q(A_c) \: \: \: \: \forall B \in \mathcal A$ with Lebesgue decomposition.

Proof that $C_{0} ^{\infty}$ bounded functions are dense in $L^{1} (\mathbb{R})$

Classical derivative of convolution via weak derivative.

Problem 15.10 of Real analysis for graduate students by R. Bass

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