Question

Does convergence in $L^1$ imply uniform boundedness on compact sets?

score 210 · Answer 1 · 2021-10-14 12:50:08

210

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Does convergence in $L^1$ imply uniform boundedness on compact sets?

Published on 14 Oct 2021 - 12:50

score 59 · Answer 2 · 2021-10-17 18:55:15

59

Views

Uniform convergence of $f_n(x)=\biggl| {{\cos (x/2)-\cos \bigl(\,(n+{1\over2})x\,\bigr)}\over 2\sin(x/2) } \biggr|$

Published on 17 Oct 2021 - 18:55

score 20 · Answer 3 · 2021-10-18 11:44:14

20

Views

Continuity Of $J:A \rightarrow \mathbb{R}$

Published on 18 Oct 2021 - 11:44

score 340 · Answer 4 · 2021-10-20 15:56:27

340

Views

Convergence of $\sum\limits_{k=1}^n\sin(kx)\frac{1}{k}$

Published on 20 Oct 2021 - 15:56

score 141 · Answer 5 · 2021-10-21 13:22:04

141

Views

Proving (non)existence of a measure space and sequence satisfying two properties

Published on 21 Oct 2021 - 13:22

score 37 · Answer 6 · 2021-10-24 13:18:15

37

Views

Let $(X,P)$ be a probability measure space. If $f_n \to f$ and $A_n \to S$ with $P(S) = 1$, is it true that $\int_X f_n1_{A_n}\,dP\to \int_X f\,dP $?

Published on 24 Oct 2021 - 13:18

score 465 · Answer 7 · 2021-10-24 14:47:51

465

Views

Book Recommendation: Series and Sequences of Functions

Published on 24 Oct 2021 - 14:47

score 76 · Answer 8 · 2021-10-24 17:41:26

76

Views

How do I prove this statement about the limes of integrals?

Published on 24 Oct 2021 - 17:41

score 39 · Answer 9 · 2021-10-29 08:08:24

39

Views

Is $f_{n}(x)=sin(\sqrt{x+4\pi^2 n^2})$ uniformly convergent on $x\in(0,b)$?

Published on 29 Oct 2021 - 8:08

score 65 · Answer 10 · 2021-10-30 00:56:18

65

Views

Existence of sequence of functions converging to integrable function in $L^1$ and pointwise

Published on 30 Oct 2021 - 0:56

score 531 · Answer 11 · 2021-10-30 10:39:01

531

Views

Uniform convergence of a sequence of functions $(f_n)$

Published on 30 Oct 2021 - 10:39

score 171 · Answer 12 · 2021-10-31 20:31:16

171

Views

Uniform Differentiability implies $f$ is $C^1$

Published on 31 Oct 2021 - 20:31

score 104 · Answer 13 · 2021-11-01 00:06:10

104

Views

Find a sequence of simple functions converging to a given function

Published on 01 Nov 2021 - 0:06

score 36 · Answer 14 · 2021-11-09 09:37:47

$x_1=\sqrt{2}, x_{n+1}=x_n+\frac 1 {x_n}$ then $\sum_{i=1}^{2021} \frac {x_i^2}{2x_ix_{i+1}-1}>\frac{2021^2}{x_{2021}^2+\frac 1 {x_{2021}^2}}.$

score 50 · Answer 15 · 2021-11-13 02:37:33

50

Views

Problem on the cyclic group generated by $T(z)=e^{2i\pi\theta} z$ with $\theta$ irrational.

Published on 13 Nov 2021 - 2:37

List Question

Does convergence in $L^1$ imply uniform boundedness on compact sets?

Uniform convergence of $f_n(x)=\biggl| {{\cos (x/2)-\cos \bigl(\,(n+{1\over2})x\,\bigr)}\over 2\sin(x/2) } \biggr|$

Continuity Of $J:A \rightarrow \mathbb{R}$

Convergence of $\sum\limits_{k=1}^n\sin(kx)\frac{1}{k}$

Proving (non)existence of a measure space and sequence satisfying two properties

Let $(X,P)$ be a probability measure space. If $f_n \to f$ and $A_n \to S$ with $P(S) = 1$, is it true that $\int_X f_n1_{A_n}\,dP\to \int_X f\,dP $?

Book Recommendation: Series and Sequences of Functions

How do I prove this statement about the limes of integrals?

Is $f_{n}(x)=sin(\sqrt{x+4\pi^2 n^2})$ uniformly convergent on $x\in(0,b)$?

Existence of sequence of functions converging to integrable function in $L^1$ and pointwise

Uniform convergence of a sequence of functions $(f_n)$

Uniform Differentiability implies $f$ is $C^1$

Find a sequence of simple functions converging to a given function

$x_1=\sqrt{2}, x_{n+1}=x_n+\frac 1 {x_n}$ then $\sum_{i=1}^{2021} \frac {x_i^2}{2x_ix_{i+1}-1}>\frac{2021^2}{x_{2021}^2+\frac 1 {x_{2021}^2}}.$

Problem on the cyclic group generated by $T(z)=e^{2i\pi\theta} z$ with $\theta$ irrational.

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