List questions from sequence-of-function

Published on 10 Jun 2020 - 17:21

205

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Why is a simple application of the Bolzano-Weierstrass Theorem not sufficient to prove Helly's Selection Theorem?

Published on 11 Jun 2020 - 19:51

252

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Uniform convergence with sine functions

Published on 12 Jun 2020 - 16:05

102

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Backwards direction of Cauchy Criterion for Sequences of Functions

Published on 21 Jun 2020 - 9:16

124

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Show that $\phi(x):=\sum_{n=1}^{\infty}\frac{(-1)^{n}}{\sqrt{n}(1+\frac{x^{2}}{n})^{n}}$ is differentiable on $\mathbb{R}$.

Published on 23 Jun 2020 - 19:58

635

Views

Proof of countable additive property of Lebesgue Integrable functions

Published on 24 Jun 2020 - 11:12

291

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Weierstrass approximation polynomial with $p^{(i)}(0)=0$

Published on 23 Feb 2026 - 4:52

97

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Find the limit of the sequence of functions: $f_n (x) = \frac{\ln (2^n +x^n)}{n}, x \ge 0$

Published on 25 Jun 2020 - 17:19

59

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Proof of the limit for the sequence of function.

Published on 25 Jun 2020 - 20:26

91

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Check the pointwise convergence and uniform convergence of a sequence of functions.

Published on 27 Jun 2020 - 2:43

34

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$L^{\infty}(\mathbb{R}^{N})$ and smallness of function

Published on 27 Jun 2020 - 6:43

101

Views

nonnegative measurable function (monoton convergence theorem)

Published on 27 Jun 2020 - 8:48

276

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A sequence of functions $f_n : [0, 1] → R$ which converges uniformly to a discontinuous function $f(x)$.

Published on 28 Jun 2020 - 1:47

69

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About convergent subsequence.

Published on 28 Jun 2020 - 3:31

118

Views

Show that $g_n$ converges to $g$ uniformly.

Published on 28 Jun 2020 - 15:13

List Question

Weierstrass' M-test in reverse

Why is a simple application of the Bolzano-Weierstrass Theorem not sufficient to prove Helly's Selection Theorem?

Uniform convergence with sine functions

Backwards direction of Cauchy Criterion for Sequences of Functions

Show that $\phi(x):=\sum_{n=1}^{\infty}\frac{(-1)^{n}}{\sqrt{n}(1+\frac{x^{2}}{n})^{n}}$ is differentiable on $\mathbb{R}$.

Proof of countable additive property of Lebesgue Integrable functions

Weierstrass approximation polynomial with $p^{(i)}(0)=0$

Find the limit of the sequence of functions: $f_n (x) = \frac{\ln (2^n +x^n)}{n}, x \ge 0$

Proof of the limit for the sequence of function.

Check the pointwise convergence and uniform convergence of a sequence of functions.

$L^{\infty}(\mathbb{R}^{N})$ and smallness of function

nonnegative measurable function (monoton convergence theorem)

A sequence of functions $f_n : [0, 1] → R$ which converges uniformly to a discontinuous function $f(x)$.

About convergent subsequence.

Show that $g_n$ converges to $g$ uniformly.

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