Prove that the set $A=\{x\in\mathbb{R}:f' \text{ exists}\}$ is Borel whenever $f$ is continuous
97735
Continuous functions are differentiable on a measurable set?
21879
Show that if $\lim_{x\to a}f'(x) = A$ then $f'(a)$ exists and equals A
96099
Every function on $\mathbb{R}^n$ that is continuous in each variable separately is Borel measurable.
48592
Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists
105652
Suppose $f: \mathbb{R} \to \mathbb{R}$ is function such that $f^3$ is continuous on $\mathbb{R}$. Prove that $f$ is continuous on $\mathbb{R}$
155923
continuity of $f(x,y)$ in $\mathbb R^2$.
122160
$f:\mathbb R \to \mathbb R$ be a continuous such that $f(f(f(x)))=x,\forall x \in \mathbb R$ , is $f(x)=x , \forall x \in \mathbb R$?
18222
Set of continuity points of a real function
95970
Let $f:[0,1] \rightarrow \mathbb{R}$ be a continuous function. If $f(0)=f(1)$ then exists $x\in [0,1]$ s.t. $f(x) = f(x+\frac{1}{2})$
52922
let $f \colon [a,b] \to \mathbb{R}$ be continuous on $[a,b]$ and..
62118
Prove $\epsilon$-$\delta$ definition of continuity implies the open set definition for real function
143105
Show that, for every real number a, the set {$x ∈ S | f(x) ≤ a$} is a closed subset of $\mathbb R^d$
24749
Monotone functions and Borel sets
143354
Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
68143
The set of convergent points of a sequence of continuous functions is Borel
131992
A problem on continuous functions
31266
Proof of "the continuous image of a connected set is connected"