Question

Why is Stolz–Cesàro is considered to be the l'Hôpital's rule for sequences?

score 156 · Answer 1 · 2020-08-09 19:15:31

156

Views

Why is Stolz–Cesàro is considered to be the l'Hôpital's rule for sequences?

Published on 09 Aug 2020 - 19:15

score 1k · Answer 2 · 2020-08-10 13:59:13

1k

Views

Prove that limit of function does not exist, if and only if sequence $f(s_n)$ is not convergent.

Published on 10 Aug 2020 - 13:59

score 132 · Answer 3 · 2020-08-10 15:54:18

132

Views

Verifying interchange of limit and integral

Published on 10 Aug 2020 - 15:54

score 23 · Answer 4 · 2020-08-12 18:33:47

23

Views

Does a sequence of functions $(f_n)$ in the probability space $L_1(\mathscr F, P)$ generate a separable $\sigma$-field?

Published on 12 Aug 2020 - 18:33

score 176 · Answer 5 · 2020-08-13 20:16:54

176

Views

To show that a certain function is measurable.

Published on 13 Aug 2020 - 20:16

score 84 · Answer 6 · 2020-08-18 11:34:02

84

Views

$f_n: \mathbb{R} \to \mathbb{R}$. If for arbitrary $\{x_n\} \to x$, $\{f_n(x_n)\} \to f(x)$, prove $f(x)$ is continuous on $\mathbb{R}$.

Published on 18 Aug 2020 - 11:34

score 953 · Answer 7 · 2020-08-24 14:53:35

953

Views

How to prove EVERY sequence converges to L in limit of function?

Published on 24 Aug 2020 - 14:53

score 60 · Answer 8 · 2020-08-25 20:43:26

60

Views

(Unusual proof) Proof that a sequence of functions converges to a function via Induction.

Published on 25 Aug 2020 - 20:43

score 73 · Answer 9 · 2020-08-26 11:06:07

73

Views

Weaker condition than uniform convergence to interchange limit and integral

Published on 26 Aug 2020 - 11:06

score 88 · Answer 10 · 2020-08-28 20:54:07

88

Views

$\sum_n(-1)^n\int_Xf_n \, d\mu=\int_X\sum_n(-1)^nf_n \, d\mu$

Published on 28 Aug 2020 - 20:54

score 63 · Answer 11 · 2020-08-29 04:06:51

63

Views

Points of differentiability of the functions $f_n(x)=|x-|x-|x-|x-.......|x-1|||||$, and their convergence

Published on 29 Aug 2020 - 4:06

score 55 · Answer 12 · 2020-09-02 17:03:05

55

Views

Sequence of a function

Published on 02 Sep 2020 - 17:03

score 44 · Answer 13 · 2020-09-03 18:24:54

44

Views

Recursion (?) With Advanced Polynomial Form

Published on 03 Sep 2020 - 18:24

score 93 · Answer 14 · 2020-09-05 20:51:19

93

Views

Correct definition of locally uniform convergence

Published on 05 Sep 2020 - 20:51

score 26 · Answer 15 · 2020-09-07 02:52:08

26

Views

sequence of continuous functions converging pointwise to reimann integrable funtion

Published on 07 Sep 2020 - 2:52

List Question

Why is Stolz–Cesàro is considered to be the l'Hôpital's rule for sequences?

Prove that limit of function does not exist, if and only if sequence $f(s_n)$ is not convergent.

Verifying interchange of limit and integral

Does a sequence of functions $(f_n)$ in the probability space $L_1(\mathscr F, P)$ generate a separable $\sigma$-field?

To show that a certain function is measurable.

$f_n: \mathbb{R} \to \mathbb{R}$. If for arbitrary $\{x_n\} \to x$, $\{f_n(x_n)\} \to f(x)$, prove $f(x)$ is continuous on $\mathbb{R}$.

How to prove EVERY sequence converges to L in limit of function?

(Unusual proof) Proof that a sequence of functions converges to a function via Induction.

Weaker condition than uniform convergence to interchange limit and integral

$\sum_n(-1)^n\int_Xf_n \, d\mu=\int_X\sum_n(-1)^nf_n \, d\mu$

Points of differentiability of the functions $f_n(x)=|x-|x-|x-|x-.......|x-1|||||$, and their convergence

Sequence of a function

Recursion (?) With Advanced Polynomial Form

Correct definition of locally uniform convergence

sequence of continuous functions converging pointwise to reimann integrable funtion

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