Question

$\lim_{r\to\infty}\frac{1}{r}\int_{-r}^r|f(x)|dx=0$ and uniform continuity implies $\lim_{x\to \pm \infty}f(x)=0$?

score 86 · Answer 1 · 2026-04-01 04:39:46

86

Views

$\lim_{r\to\infty}\frac{1}{r}\int_{-r}^r|f(x)|dx=0$ and uniform continuity implies $\lim_{x\to \pm \infty}f(x)=0$?

Published on 01 Apr 2026 - 4:39

score 3.5k · Answer 2 · 2017-12-08 05:38:15

3.5k

Views

A function is uniformly differentiable if its derivative is uniformly continuous?

Published on 08 Dec 2017 - 5:38

score 219 · Answer 3 · 2017-12-10 22:31:33

219

Views

Prove that $f$ is uniformly continuous in a bounded metric space, E.

Published on 10 Dec 2017 - 22:31

score 945 · Answer 4 · 2017-12-13 07:25:22

945

Views

f is continuous on $(X,\tau)$ iff pre-image of set’s interior is subset of pre-interior of set

Published on 13 Dec 2017 - 7:25

score 2.7k · Answer 5 · 2017-12-13 19:27:01

2.7k

Views

Identity function is a homeomorphism iff topologies are equal

Published on 13 Dec 2017 - 19:27

score 61 · Answer 6 · 2026-03-27 21:34:42

61

Views

Modulus of continuity of Radial Basis Function

Published on 27 Mar 2026 - 21:34

score 92 · Answer 7 · 2017-12-15 00:24:17

92

Views

$f: \mathbb R \to \mathbb R$ differentiable function s.t. $|f'(x)| \le 100$ for all $x \in \mathbb R$. Prove $f$ uniformly continuous.

Published on 15 Dec 2017 - 0:24

score 472 · Answer 8 · 2017-12-15 06:39:36

472

Views

If a function $f: [0,1] \to \mathbb R$ is continuous, does it mean that it's uniformly continuous?

Published on 15 Dec 2017 - 6:39

score 60 · Answer 9 · 2017-12-15 08:40:43

60

Views

Continuity at a particular point? Uniform continuity everywhere?

Published on 15 Dec 2017 - 8:40

score 93 · Answer 10 · 2017-12-15 16:49:15

93

Views

Is this proof of the uniform continuity of $\sqrt{x}$ correct?

Published on 15 Dec 2017 - 16:49

score 148 · Answer 11 · 2017-12-16 15:56:01

148

Views

If f is uniformly continuous in R. Then g (x, y) = f (x) -f (y) is uniformly continuous in R^2

Published on 16 Dec 2017 - 15:56

score 89 · Answer 12 · 2017-12-19 05:17:18

89

Views

Argue that $f$ is not uniformly continuous

Published on 19 Dec 2017 - 5:17

score 84 · Answer 13 · 2017-12-19 19:07:11

84

Views

Proving that $x^2$ is not unifromly continuous on $\mathbb{R}$

Published on 19 Dec 2017 - 19:07

score 108 · Answer 14 · 2017-12-20 09:49:11

108

Views

Interrelation between continuity and differentiability?

Published on 20 Dec 2017 - 9:49

score 108 · Answer 15 · 2017-12-22 07:14:11

108

Views

Is the function $f(x) = |x|$ uniformly continuous on the interval $ (0,1] $?

Published on 22 Dec 2017 - 7:14

List Question

$\lim_{r\to\infty}\frac{1}{r}\int_{-r}^r|f(x)|dx=0$ and uniform continuity implies $\lim_{x\to \pm \infty}f(x)=0$?

A function is uniformly differentiable if its derivative is uniformly continuous?

Prove that $f$ is uniformly continuous in a bounded metric space, E.

f is continuous on $(X,\tau)$ iff pre-image of set’s interior is subset of pre-interior of set

Identity function is a homeomorphism iff topologies are equal

Modulus of continuity of Radial Basis Function

$f: \mathbb R \to \mathbb R$ differentiable function s.t. $|f'(x)| \le 100$ for all $x \in \mathbb R$. Prove $f$ uniformly continuous.

If a function $f: [0,1] \to \mathbb R$ is continuous, does it mean that it's uniformly continuous?

Continuity at a particular point? Uniform continuity everywhere?

Is this proof of the uniform continuity of $\sqrt{x}$ correct?

If f is uniformly continuous in R. Then g (x, y) = f (x) -f (y) is uniformly continuous in R^2

Argue that $f$ is not uniformly continuous

Proving that $x^2$ is not unifromly continuous on $\mathbb{R}$

Interrelation between continuity and differentiability?

Is the function $f(x) = |x|$ uniformly continuous on the interval $ (0,1] $?

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