Let $f : [0, +\infty) \rightarrow \mathbb{R}$ be uniformly continuous. Show that $f$ has sublinear growth
14067
If f uniformly continous then $|f(x)|\leq C\cdot (1+|x|)$ for constant C
117486
Limit of uniformly continuous functions with convergent improper integrals.
24017
Let $f: \Bbb R \to [0,\infty)$ be a continuous function such that $g(x)=(f(x))^2$ is uniformly continuous. Which of the following is always true?
20404
Prove that $f$ continuous and $\int_a^\infty |f(x)|\;dx$ finite imply $\lim\limits_{ x \to \infty } f(x)=0$
153271
Fourier transform is uniformly continuous
15727
show that if $f$ is uniformly differentiable then prove that $f'$ is continuous
150896
Show that $\lim_{p \to \infty} \| f \|_p = \| f \|_\infty$
131060
Is $\sqrt{x}$ uniformly continuous in $\mathbb{R}^+$?
112211
Show an increasing function f from omega_1 to R is eventually constant
97256
For $f$ continuous, show $\lim_{n\to\infty} n\int_0^1 f(x)x^n\,dx = f(1).$
813
$f$ uniformly continuous and $\int_a^\infty f(x)\,dx$ converges imply $\lim_{x \to \infty} f(x) = 0$
156905
Prove $f_n$ has a uniformly convergent subsequence on $[0,1]$.
125723
Proof of $Y=F_X(X)$ being uniformly distributed on $[0,1]$ for arbitrary continuous $F_X$
134838
Uniform continuity of $f(x)=x^{2/3}\log x$ on $[0, \infty)$
113740
Find a uniformly continuous function such that $a_{n+1}=f(a_n)$
127449
Uniform continuous of $f(x,y) = \sin(x^2+y)$
28730
product of two uniformly continuous functions is uniformly continuous