if $f:[0,1] \to \mathbb{R}$ is increasing, show that $f$ is the pointwise limit of a sequence of continuous functions over $[0,1]$
99431
Increasing functions are Baire one
112409
If $f$ is continuous and $f'(x)\ge 0$, outside of a countable set, then $f$ is increasing
20404
Prove that $f$ continuous and $\int_a^\infty |f(x)|\;dx$ finite imply $\lim\limits_{ x \to \infty } f(x)=0$
94737
How to show $f$ is continuous at $x$ IFF for any sequence ${x_n}$ in $X$ converging to $x$ the sequence $f(x_n)$ converges in $Y$ to $f(x)$
60282
Prove that $f_n$ converges uniformly on $\mathbb{R}$
28191
How to show that a set of discontinuous points of an increasing function is at most countable
78319
Show that $x \mapsto \frac{f(x)}{x}$ is strictly increasing on (0,1) given that f '(x) is strictly increasing on (0,1) and that f(0)=0
65033
Prove inverse of strictly monotone increasing function is continuous over the range of original function
47693
Applying Arzela-Ascoli to show pointwise convergence on $\mathbb{R}$.
15579
Show that $f$ is uniformly continuous if limit exists
150346
If $f$ is an increasing function defined on $[a,b]$ . Then, $f$ has countable number of discontinuities
95469
Suppose $f:[0,1] \Rightarrow \mathbb{R}$ is continuous and $\int_0^x f(x)dx = \int_x^1 f(x)dx$. Prove that $f(x) = 0$ for all $x$
82405
For f continuous on $[0,1]$, show that there exist points $\alpha_k$ such that $\sum \limits_{k=1}^n \frac{1}{f'(\alpha_k)} = n $
93637
Does this sequence converge pointwise and/or in $L^1$?
110415
Proving a sequence of step functions converges pointwise to a function $f$.
71140
Pointwise limit of the sequence of continuously differentiable functions defined inductively.
131992
A problem on continuous functions