Question

If $(f_n)_n\rightarrow f$ almost everywhere and in measure, does $(f_n)_n\rightarrow f$ almost uniformly?

score 650 · Answer 1 · 2026-03-29 05:12:14

650

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If $(f_n)_n\rightarrow f$ almost everywhere and in measure, does $(f_n)_n\rightarrow f$ almost uniformly?

Published on 29 Mar 2026 - 5:12

score 160 · Answer 2 · 2026-04-16 06:28:17

160

Views

Let $f$ be continuous on $[-1,1]$, Show that $g_n \to f$ uniformly on $[-1,1]$

Published on 16 Apr 2026 - 6:28

score 69 · Answer 3 · 2026-04-16 23:40:51

69

Views

Test the uniform convergence of the series $\sum_{n=1}^\infty \frac{2^nx^{2^n-1}}{1+x^{2n}} $

Published on 16 Apr 2026 - 23:40

score 777 · Answer 4 · 2026-04-17 01:40:50

777

Views

Test uniform convergence of the series $\sum_{n=1}^{\infty}\frac{x}{(n+x^2)^2}$

Published on 17 Apr 2026 - 1:40

score 46 · Answer 5 · 2026-04-11 20:21:55

46

Views

In $(\mathbb{Z}, \mathcal{P}(\mathbb{Z}), \mu)$, convergence in measure is equivalent to uniform convergence.

Published on 11 Apr 2026 - 20:21

score 2.9k · Answer 6 · 2026-04-15 03:33:50

2.9k

Views

Uniform Convergence of $(\sin x)^n$

Published on 15 Apr 2026 - 3:33

score 1k · Answer 7 · 2026-04-16 14:50:29

1k

Views

which of the following statement is correct?

Published on 16 Apr 2026 - 14:50

score 1.1k · Answer 8 · 2026-03-29 03:20:20

1.1k

Views

Dominated a.e. convergence implies almost uniform convergence

Published on 29 Mar 2026 - 3:20

score 179 · Answer 9 · 2026-04-13 23:57:00

179

Views

How to show $\sum\limits_{n=0}^\infty \frac{{x^2}}{(1+x^2)^n}$ is uniformly convergent over $[-1,1]$.

Published on 13 Apr 2026 - 23:57

score 98 · Answer 10 · 2026-04-16 11:06:37

98

Views

Value of sum and uniform convergence of $\sum_{n=0}^{\infty} (1-\log x)\log^{n}x$?

Published on 16 Apr 2026 - 11:06

score 1k · Answer 11 · 2026-04-15 04:53:43

1k

Views

Uniform convergence of derivative implies pointwise convergence of sequence of functions

Published on 15 Apr 2026 - 4:53

score 622 · Answer 12 · 2026-04-15 21:11:49

622

Views

Uniform Integrability of $M^2$ if $M$ is a martingale.

Published on 15 Apr 2026 - 21:11

score 564 · Answer 13 · 2026-04-12 22:23:04

564

Views

To show function converges to a continuous function but not uniformly

Published on 12 Apr 2026 - 22:23

score 57 · Answer 14 · 2026-04-15 18:07:17

57

Views

Uniform convergence of $f_n (x) = \frac{1+x^n}{n+x^{2n}}$ on $\mathbb{R}$

Published on 15 Apr 2026 - 18:07

score 230 · Answer 15 · 2026-04-15 18:59:01

230

Views

Prove $\sum_{n=1}^\infty\frac{(-1)^n}{\sqrt{n}}\arctan(\frac{x}{\sqrt{n}})$ converges and defines a continuously differentiable function

Published on 15 Apr 2026 - 18:59

List Question

If $(f_n)_n\rightarrow f$ almost everywhere and in measure, does $(f_n)_n\rightarrow f$ almost uniformly?

Let $f$ be continuous on $[-1,1]$, Show that $g_n \to f$ uniformly on $[-1,1]$

Test the uniform convergence of the series $\sum_{n=1}^\infty \frac{2^nx^{2^n-1}}{1+x^{2n}} $

Test uniform convergence of the series $\sum_{n=1}^{\infty}\frac{x}{(n+x^2)^2}$

In $(\mathbb{Z}, \mathcal{P}(\mathbb{Z}), \mu)$, convergence in measure is equivalent to uniform convergence.

Uniform Convergence of $(\sin x)^n$

which of the following statement is correct?

Dominated a.e. convergence implies almost uniform convergence

How to show $\sum\limits_{n=0}^\infty \frac{{x^2}}{(1+x^2)^n}$ is uniformly convergent over $[-1,1]$.

Value of sum and uniform convergence of $\sum_{n=0}^{\infty} (1-\log x)\log^{n}x$?

Uniform convergence of derivative implies pointwise convergence of sequence of functions

Uniform Integrability of $M^2$ if $M$ is a martingale.

To show function converges to a continuous function but not uniformly

Uniform convergence of $f_n (x) = \frac{1+x^n}{n+x^{2n}}$ on $\mathbb{R}$

Prove $\sum_{n=1}^\infty\frac{(-1)^n}{\sqrt{n}}\arctan(\frac{x}{\sqrt{n}})$ converges and defines a continuously differentiable function

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