Question

Does the convergence to 0 in $L^2(0,T;L^2(K))$ for all compact $K \subset \mathbb{R}^{d}$ imply the convergence in $L^2(0,T;L^2(\mathbb{R}^{d}))$?

score 37 · Answer 1 · 2020-07-07 03:09:03

37

Views

Does the convergence to 0 in $L^2(0,T;L^2(K))$ for all compact $K \subset \mathbb{R}^{d}$ imply the convergence in $L^2(0,T;L^2(\mathbb{R}^{d}))$?

Published on 07 Jul 2020 - 3:09

score 132 · Answer 2 · 2020-07-07 10:36:58

132

Views

Applications of dominated convergence theorem for Lebesgue integrals

Published on 07 Jul 2020 - 10:36

score 285 · Answer 3 · 2020-07-07 10:37:54

285

Views

How is the sum of two Lebesgue integrable functions?

Published on 07 Jul 2020 - 10:37

score 113 · Answer 4 · 2020-07-07 11:24:22

113

Views

How is the product of two Lebesgue integrable functions?

Published on 07 Jul 2020 - 11:24

score 44 · Answer 5 · 2020-07-07 16:54:09

44

Views

Convergence to 0 of certain integral by DCT

Published on 07 Jul 2020 - 16:54

score 91 · Answer 6 · 2020-07-08 01:15:50

91

Views

Show the sequence $f_n(x)=\frac{1}{n}\chi_{[0,n]}$ has no weakly convergent subsequence in $L^1$.

Published on 08 Jul 2020 - 1:15

score 79 · Answer 7 · 2020-07-08 17:41:57

79

Views

An application of Fubini theorem from Analysis

Published on 08 Jul 2020 - 17:41

score 53 · Answer 8 · 2020-07-08 17:59:37

53

Views

$ \lim_{n\to \infty} \int_0^1 e^{i\cdot n\cdot p(x)}~dx=0$ where $p(x)$ is a nonconstant polynomial with real coefficients

Published on 08 Jul 2020 - 17:59

score 737 · Answer 9 · 2020-07-08 18:12:49

737

Views

Dominated convergence theorem and Cauchy's integral formula

Published on 08 Jul 2020 - 18:12

score 334 · Answer 10 · 2020-07-08 19:09:50

334

Views

Using Chebyshev's Inequality with Lebesgue Integral

Published on 08 Jul 2020 - 19:09

score 85 · Answer 11 · 2020-07-08 19:18:57

85

Views

Sine integral and Lebesgue integration

Published on 08 Jul 2020 - 19:18

score 195 · Answer 12 · 2026-03-27 06:06:36

195

Views

Integrate indicator function by Lebesgue measure

Published on 27 Mar 2026 - 6:06

score 89 · Answer 13 · 2026-04-06 19:03:27

89

Views

$f\in L^2[0,1]$ iff $f\in L^1[0,1]$ and there is nondecreasing $g$ with $|\int_a^b f(x)dx|^2 \leq (g(b)-g(a))(b-a)$ for $0\leq a\leq b\leq 1$

Published on 06 Apr 2026 - 19:03

score 33 · Answer 14 · 2020-07-09 04:30:34

33

Views

Lebesgue measurability of $f \circ T$ when $T \notin GL_n(\mathbb{R})$

Published on 09 Jul 2020 - 4:30

score 31 · Answer 15 · 2020-07-10 06:06:27

31

Views

Concept of integration over the probability density function (pdf) $f\left( {r,\theta } \right)$.

Published on 10 Jul 2020 - 6:06

List Question

Does the convergence to 0 in $L^2(0,T;L^2(K))$ for all compact $K \subset \mathbb{R}^{d}$ imply the convergence in $L^2(0,T;L^2(\mathbb{R}^{d}))$?

Applications of dominated convergence theorem for Lebesgue integrals

How is the sum of two Lebesgue integrable functions?

How is the product of two Lebesgue integrable functions?

Convergence to 0 of certain integral by DCT

Show the sequence $f_n(x)=\frac{1}{n}\chi_{[0,n]}$ has no weakly convergent subsequence in $L^1$.

An application of Fubini theorem from Analysis

$ \lim_{n\to \infty} \int_0^1 e^{i\cdot n\cdot p(x)}~dx=0$ where $p(x)$ is a nonconstant polynomial with real coefficients

Dominated convergence theorem and Cauchy's integral formula

Using Chebyshev's Inequality with Lebesgue Integral

Sine integral and Lebesgue integration

Integrate indicator function by Lebesgue measure

$f\in L^2[0,1]$ iff $f\in L^1[0,1]$ and there is nondecreasing $g$ with $|\int_a^b f(x)dx|^2 \leq (g(b)-g(a))(b-a)$ for $0\leq a\leq b\leq 1$

Lebesgue measurability of $f \circ T$ when $T \notin GL_n(\mathbb{R})$

Concept of integration over the probability density function (pdf) $f\left( {r,\theta } \right)$.

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