Question

Domain Schrödinger equation

score 100 · Answer 1 · 2014-08-09 23:04:15

100

Views

Domain Schrödinger equation

Published on 09 Aug 2014 - 23:04

score 1.2k · Answer 2 · 2014-08-09 23:05:46

1.2k

Views

Why define the Lebesgue-Integral just for measurable functions?

Published on 09 Aug 2014 - 23:05

score 217 · Answer 3 · 2014-08-11 18:08:38

217

Views

Limiting variable in interval: Lebesgue Dominated Convergence

Published on 11 Aug 2014 - 18:08

score 46 · Answer 4 · 2014-08-11 20:46:00

46

Views

What is the integral of $\int_{\mathbb{N}} s d\mu$ where $\mu$ is the counting measure on $\mathbb{P}(\mathbb{N})$?

Published on 11 Aug 2014 - 20:46

score 182 · Answer 5 · 2026-03-31 18:42:14

182

Views

Series converges but term by term integration not valid?

Published on 31 Mar 2026 - 18:42

score 82 · Answer 6 · 2014-08-13 07:30:03

82

Views

Is a $L^1$-function which is linear near the origin in $L^p$?

Published on 13 Aug 2014 - 7:30

score 107 · Answer 7 · 2014-08-15 09:15:57

107

Views

Integral $ \lim_{k \rightarrow \infty} \int_{\mathbb{R}^n} \chi_{B_k} f \mathrm{d}\lambda_n(x) $ (Lebesgue)

Published on 15 Aug 2014 - 9:15

score 165 · Answer 8 · 2026-03-25 17:39:03

165

Views

Lebesgue-integrable and existence of integral

Published on 25 Mar 2026 - 17:39

score 141 · Answer 9 · 2014-08-19 15:20:08

141

Views

If the integral $\int_0^\infty xf(x)\,dx$ converges, so does $\sum_{n=1}^{\infty}\int_0^{\infty}f(x+n)\, dx$

Published on 19 Aug 2014 - 15:20

score 1.4k · Answer 10 · 2026-04-01 02:07:15

1.4k

Views

Characterisation of one-dimensional Sobolev space

Published on 01 Apr 2026 - 2:07

score 354 · Answer 11 · 2014-08-21 23:43:00

354

Views

Prove that for any $1 < p < ∞$ there exists a function $f ∈ L_p(μ)$ such that $f \notin L_q(μ)$ for any $q > p.$

Published on 21 Aug 2014 - 23:43

score 139 · Answer 12 · 2014-08-22 01:03:23

139

Views

Is $\frac{\mathrm d}{\mathrm dx} \sin x/x = \cos x/x - \sin x/x^2$ Lebesgue integrable?

Published on 22 Aug 2014 - 1:03

score 700 · Answer 13 · 2014-08-25 17:36:41

700

Views

Prove that $\lim_{n \rightarrow \infty} \frac{1}{n}\int^n_0xf(x)dx = 0$

Published on 25 Aug 2014 - 17:36

score 1.8k · Answer 14 · 2014-08-25 21:59:48

1.8k

Views

Measurability of product of Borel measurable functions with different domains?

Published on 25 Aug 2014 - 21:59

score 594 · Answer 15 · 2014-08-26 18:41:56

594

Views

Show that for any $g \in L_{p'}(E)$, where $p'$ is the conjugate of $p$, $\lim_{k \rightarrow \infty}\int_Ef_k(x)g(x)dx = \int_Ef(x)g(x)dx$

Published on 26 Aug 2014 - 18:41

List Question

Domain Schrödinger equation

Why define the Lebesgue-Integral just for measurable functions?

Limiting variable in interval: Lebesgue Dominated Convergence

What is the integral of $\int_{\mathbb{N}} s d\mu$ where $\mu$ is the counting measure on $\mathbb{P}(\mathbb{N})$?

Series converges but term by term integration not valid?

Is a $L^1$-function which is linear near the origin in $L^p$?

Integral $ \lim_{k \rightarrow \infty} \int_{\mathbb{R}^n} \chi_{B_k} f \mathrm{d}\lambda_n(x) $ (Lebesgue)

Lebesgue-integrable and existence of integral

If the integral $\int_0^\infty xf(x)\,dx$ converges, so does $\sum_{n=1}^{\infty}\int_0^{\infty}f(x+n)\, dx$

Characterisation of one-dimensional Sobolev space

Prove that for any $1 < p < ∞$ there exists a function $f ∈ L_p(μ)$ such that $f \notin L_q(μ)$ for any $q > p.$

Is $\frac{\mathrm d}{\mathrm dx} \sin x/x = \cos x/x - \sin x/x^2$ Lebesgue integrable?

Prove that $\lim_{n \rightarrow \infty} \frac{1}{n}\int^n_0xf(x)dx = 0$

Measurability of product of Borel measurable functions with different domains?

Show that for any $g \in L_{p'}(E)$, where $p'$ is the conjugate of $p$, $\lim_{k \rightarrow \infty}\int_Ef_k(x)g(x)dx = \int_Ef(x)g(x)dx$

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