f uniformly Lipschitz, integral from 0 to inf of |f(x)|  inf.
813
$f$ uniformly continuous and $\int_a^\infty f(x)\,dx$ converges imply $\lim_{x \to \infty} f(x) = 0$
62048
Proving a Lipschitz function is continuous
107727
$m\{x\in [0,1]:f'(x)=0\}>0$
115495
Prove $\int _0^\infty f^2 dx \leq \cdots $ for $f$ convex
40297
Proof of uniform limit of Continuous Functions
50730
Integral of bounded continuous function on $R$
28619
Bound on integral implies bound on function
10408
Uniformly convergence of $f_{n+1}(x)= \int^x_0 f_n(t)dt$
75735
Let $f$ be a continuous function on an interval around $0$ and let $a_i=f(\frac{1}{i})$ (for large enough $i$)
153063
Uniform convergence of $f_n(x)=nx^n(1-x)$ for $x \in [0,1]$?
144957
Uniform convergence of a function
7945
Approximate $|x|$ with a smooth function
33488
A uniformly continuous function such that the derivative is not bounded and is not defined on a compact?
80622
Lebesgue integral uniform convergence
150305
$f_{n+1}(x):= \int_a ^x f_n(t)dt$, $\sum_{m=1} ^{\infty} f_m(x)$ is uniformly convergent
76155
Verification of extension result for Lipschitz functions
123981
Is it possible to write any bounded continuous function as a uniform limit of smooth functions