Question

Point wise and uniform convergence of sequences of functions

score 41 · Answer 1 · 2026-04-13 14:31:25

41

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Point wise and uniform convergence of sequences of functions

Published on 13 Apr 2026 - 14:31

score 55 · Answer 2 · 2026-04-14 02:28:46

55

Views

Uniform convergence of sequence of differentiable functions

Published on 14 Apr 2026 - 2:28

score 43 · Answer 3 · 2026-04-11 09:25:15

43

Views

Interval of pointwise convergence of a function series

Published on 11 Apr 2026 - 9:25

score 75 · Answer 4 · 2026-04-15 11:34:09

75

Views

Is converge pointwise with this property implies uniform convergence?

Published on 15 Apr 2026 - 11:34

score 47 · Answer 5 · 2026-04-15 21:54:46

47

Views

Spivak, Ch. 24, Problem 1a: Does $\sqrt[n]{x}$ converge pointwise to $f(x)=1, x\in (0,1]$, $f(0)=0$ on $(0,1]$ or on $[0,1]$?

Published on 15 Apr 2026 - 21:54

score 111 · Answer 6 · 2026-04-16 12:29:27

111

Views

Let $f_n\to f$ pointwise for measurable functions $f_n$. Is $f$ measurable?

Published on 16 Apr 2026 - 12:29

score 333 · Answer 7 · 2026-04-14 01:40:24

333

Views

$\Gamma$-convergence vs. uniform convergence: conditions for convergence of minimizers of functionals

Published on 14 Apr 2026 - 1:40

score 100 · Answer 8 · 2026-04-14 10:21:32

100

Views

How do we show that $\sin{x}$ is in fact equal to the infinite series $\sum\limits_{n=0}^\infty (-1)^n\frac{x^{2n+1}}{(2n+1)!}$?

Published on 14 Apr 2026 - 10:21

score 73 · Answer 9 · 2026-04-16 04:41:24

73

Views

Interval of convergence of the infinite series $\sum_{n=1}^{\infty} \frac{x^n}{1+x^n}$

Published on 16 Apr 2026 - 4:41

score 68 · Answer 10 · 2026-04-16 11:06:41

68

Views

Finding the interval of convergence of the infinite series $\sum_{n=1}^{\infty}\frac{2^n + x^n}{1+3^n x^n}$

Published on 16 Apr 2026 - 11:06

score 115 · Answer 11 · 2026-04-14 03:40:09

115

Views

If $f_n \to f$ and for every $n > 0$ $f_n$ is uniformly continuous then f is uniformly continuous. Where did my proof fail?

Published on 14 Apr 2026 - 3:40

score 235 · Answer 12 · 2026-04-15 16:32:58

235

Views

intuition for $\lim_{n \to \infty} f_n'(x) \ne f'(x)$ (Tom Apostol's exercise $11.7.18$)

Published on 15 Apr 2026 - 16:32

score 634 · Answer 13 · 2026-04-13 10:22:09

634

Views

If $(f_n)$ converges pointwise to $f$, then $f$ is uniformly continuous

Published on 13 Apr 2026 - 10:22

score 91 · Answer 14 · 2026-04-16 01:24:26

91

Views

Uniform integrability and $L^1$ convergence of $(1/X_n)$

Published on 16 Apr 2026 - 1:24

score 145 · Answer 15 · 2026-04-10 07:19:48

145

Views

Fourier series pointwise convergence

Published on 10 Apr 2026 - 7:19

List Question

Point wise and uniform convergence of sequences of functions

Uniform convergence of sequence of differentiable functions

Interval of pointwise convergence of a function series

Is converge pointwise with this property implies uniform convergence?

Spivak, Ch. 24, Problem 1a: Does $\sqrt[n]{x}$ converge pointwise to $f(x)=1, x\in (0,1]$, $f(0)=0$ on $(0,1]$ or on $[0,1]$?

Let $f_n\to f$ pointwise for measurable functions $f_n$. Is $f$ measurable?

$\Gamma$-convergence vs. uniform convergence: conditions for convergence of minimizers of functionals

How do we show that $\sin{x}$ is in fact equal to the infinite series $\sum\limits_{n=0}^\infty (-1)^n\frac{x^{2n+1}}{(2n+1)!}$?

Interval of convergence of the infinite series $\sum_{n=1}^{\infty} \frac{x^n}{1+x^n}$

Finding the interval of convergence of the infinite series $\sum_{n=1}^{\infty}\frac{2^n + x^n}{1+3^n x^n}$

If $f_n \to f$ and for every $n > 0$ $f_n$ is uniformly continuous then f is uniformly continuous. Where did my proof fail?

intuition for $\lim_{n \to \infty} f_n'(x) \ne f'(x)$ (Tom Apostol's exercise $11.7.18$)

If $(f_n)$ converges pointwise to $f$, then $f$ is uniformly continuous

Uniform integrability and $L^1$ convergence of $(1/X_n)$

Fourier series pointwise convergence

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