List questions from sequence-of-function

Published on 26 Apr 2022 - 12:43

312

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Convergence of derivatives.

Published on 29 Apr 2022 - 14:59

42

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Intuition behind the proof that pointwise limit of measurable function is measurable.

Published on 07 May 2022 - 15:36

22

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Why is the definition of lub failing in the sequence $\left\{ \frac{1}{n}\right\}$?

Published on 08 May 2022 - 23:47

26

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Compute sup norm of sequence of functions.

Published on 13 May 2022 - 12:34

37

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Is there any $K_t^{\epsilon}\to \mathbf{1}_{[0,t]}$ such that $\frac{d}{dt}\|K_t^{\epsilon}\|^2\to 1$?

Published on 17 May 2022 - 9:03

57

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Is the limit of this sequence Lipschitz-continuous?

Published on 26 May 2022 - 19:14

72

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Convergence of integrals without the dominated convergence theorem

Published on 26 Feb 2026 - 11:16

241

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L1 and L2 norm not equivalent on sequence of functions where H^1 norm is uniformly bounded

Published on 31 May 2022 - 20:23

93

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Sequence of functions $(f_n)$ with $|f_{n+1}(x)-f_n(x)| \le \frac{1}{2^n+x^2}$ is uniformly convergent in $\Bbb R$

Published on 13 Jun 2022 - 13:12

571

Views

Equivalence of two norms on $C[0,1]$

Published on 13 Jun 2022 - 16:16

49

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How can I show this function sequence is Cauchy in $C([-1,1])$ with $||f|| = \max|f(x)|$?

Published on 17 Jun 2022 - 9:27

137

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Smoothness of limit of sequence of functions when sequence of derivatives converges to a continuous function

Published on 17 Jun 2022 - 19:34

34

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Show whether the sequence is a Cauchy Sequence

Published on 20 Jun 2022 - 11:39

790

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Let $f_n:(0,1)\to\Bbb{R}$ be a sequence of continuous functions such that $\forall$ cauchy sequence $\{x_n\}$ in $(0,1)$, $f_n(x_n)\to 0$.

Published on 20 Jun 2022 - 20:06

List Question

Question about final sequence in the diagonal trick.

Convergence of derivatives.

Intuition behind the proof that pointwise limit of measurable function is measurable.

Why is the definition of lub failing in the sequence $\left\{ \frac{1}{n}\right\}$?

Compute sup norm of sequence of functions.

Is there any $K_t^{\epsilon}\to \mathbf{1}_{[0,t]}$ such that $\frac{d}{dt}\|K_t^{\epsilon}\|^2\to 1$?

Is the limit of this sequence Lipschitz-continuous?

Convergence of integrals without the dominated convergence theorem

L1 and L2 norm not equivalent on sequence of functions where H^1 norm is uniformly bounded

Sequence of functions $(f_n)$ with $|f_{n+1}(x)-f_n(x)| \le \frac{1}{2^n+x^2}$ is uniformly convergent in $\Bbb R$

Equivalence of two norms on $C[0,1]$

How can I show this function sequence is Cauchy in $C([-1,1])$ with $||f|| = \max|f(x)|$?

Smoothness of limit of sequence of functions when sequence of derivatives converges to a continuous function

Show whether the sequence is a Cauchy Sequence

Let $f_n:(0,1)\to\Bbb{R}$ be a sequence of continuous functions such that $\forall$ cauchy sequence $\{x_n\}$ in $(0,1)$, $f_n(x_n)\to 0$.

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