Question

Could someone elaborate on the difference between different definitions of stochastic equicontinuity (Asymptotically uniformly equicontinuous)?)

score 235 · Answer 1 · 2019-10-23 12:25:11

235

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Could someone elaborate on the difference between different definitions of stochastic equicontinuity (Asymptotically uniformly equicontinuous)?)

Published on 23 Oct 2019 - 12:25

score 1.4k · Answer 2 · 2019-11-21 04:59:07

1.4k

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prove/disprove: the functions $f_n(x)=\cos(x+n)+\ln\left(1+\frac{\sin^2(n^nx)}{\sqrt{n+2}}\right)$ are uniformly equicontinuous

Published on 21 Nov 2019 - 4:59

score 104 · Answer 3 · 2019-11-21 15:24:36

104

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Equicontinuity + Compact $\rightarrow$ Uniform eqcontinuity

Published on 21 Nov 2019 - 15:24

score 60 · Answer 4 · 2019-11-22 02:02:39

60

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Show that $F=\{f_n\;|\; n\in N, \; f_n:[0,1]\to R \; \ni f_n(x)=x^n\}$ is not equicontinuous at $x=0$

Published on 22 Nov 2019 - 2:02

score 428 · Answer 5 · 2019-11-22 03:35:49

428

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Show that $\{\sin(nx) \; \mid \; n \in N\}$ is not equicontinuous at $x=1$

Published on 22 Nov 2019 - 3:35

score 618 · Answer 6 · 2019-11-23 16:38:54

618

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Show the Set of Polynomials of Degree $\le n$, Uniformly Bounded in a compact $C$ is Equicontinuous in $C$

Published on 23 Nov 2019 - 16:38

score 60 · Answer 7 · 2019-11-30 22:16:26

60

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Prove if exists $M>0$ such that $|f'(t)|\leq M\,\forall\,f\in F$ and for all $t\in(a,b)$ then $F$ is equicontinuous.

Published on 30 Nov 2019 - 22:16

score 48 · Answer 8 · 2019-12-10 16:55:13

Let $E=[0,1]$, $K>0$ be a given constant, and $F$ be a set of continous functions on compact interval E such that $|f(x)-f(y)|\leq K|x-y|$

score 240 · Answer 9 · 2020-01-04 10:19:06

240

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Equicontinuity of set of functions.

Published on 04 Jan 2020 - 10:19

score 46 · Answer 10 · 2020-01-13 03:47:42

46

Views

How equicontinuity follows in following proposition?

Published on 13 Jan 2020 - 3:47

score 817 · Answer 11 · 2020-01-26 16:50:45

817

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Equicontinuous on a compact set implies uniform equicontinuous

Published on 26 Jan 2020 - 16:50

score 34 · Answer 12 · 2020-02-07 14:37:09

34

Views

Prove the equicontinuity of family of $C^1$ functions

Published on 07 Feb 2020 - 14:37

score 156 · Answer 13 · 2020-02-09 04:31:32

156

Views

Equicontinuous Functions and Non-continuous functions uniformly bounded functions

Published on 09 Feb 2020 - 4:31

score 86 · Answer 14 · 2020-02-13 10:20:47

86

Views

Prove the relative compactness of a family of $C^1$ functions

Published on 13 Feb 2020 - 10:20

score 295 · Answer 15 · 2020-02-19 03:20:21

295

Views

Application of Arzela-Ascoli Theorem, proving uniform boundedness and equicontinuity

Published on 19 Feb 2020 - 3:20

List Question

Could someone elaborate on the difference between different definitions of stochastic equicontinuity (Asymptotically uniformly equicontinuous)?)

prove/disprove: the functions $f_n(x)=\cos(x+n)+\ln\left(1+\frac{\sin^2(n^nx)}{\sqrt{n+2}}\right)$ are uniformly equicontinuous

Equicontinuity + Compact $\rightarrow$ Uniform eqcontinuity

Show that $F=\{f_n\;|\; n\in N, \; f_n:[0,1]\to R \; \ni f_n(x)=x^n\}$ is not equicontinuous at $x=0$

Show that $\{\sin(nx) \; \mid \; n \in N\}$ is not equicontinuous at $x=1$

Show the Set of Polynomials of Degree $\le n$, Uniformly Bounded in a compact $C$ is Equicontinuous in $C$

Prove if exists $M>0$ such that $|f'(t)|\leq M\,\forall\,f\in F$ and for all $t\in(a,b)$ then $F$ is equicontinuous.

Let $E=[0,1]$, $K>0$ be a given constant, and $F$ be a set of continous functions on compact interval E such that $|f(x)-f(y)|\leq K|x-y|$

Equicontinuity of set of functions.

How equicontinuity follows in following proposition?

Equicontinuous on a compact set implies uniform equicontinuous

Prove the equicontinuity of family of $C^1$ functions

Equicontinuous Functions and Non-continuous functions uniformly bounded functions

Prove the relative compactness of a family of $C^1$ functions

Application of Arzela-Ascoli Theorem, proving uniform boundedness and equicontinuity

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