Show if $f(x+y)=f(x)+f(y)$ for all $x,y$ and $f$ is Lebesgue measurable, then $f$ is continuous.
98823
Let $g:\mathbb{R}\to\mathbb{R}$ be a measurable function such that $g(x+y) =g(x)+g(y).$ Then $g(x) = g(1)x$ .
155923
continuity of $f(x,y)$ in $\mathbb R^2$.
37966
If $f$ is continuous and $f(x+y) = f(x)+f(y)$, then $f(x) = cx$ for all $x \in \mathbb{R}$
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.
72847
Does $f(x)$ is continuous and $f = 0$ a.e. imply $f=0$ everywhere?
66772
$f(f(x)f(y))+f(x+y)=f(xy)$
68048
Prove that if $f$ is differentiable on $[a,b]$ and $f'$ is monotonic on $[a,b]$ , $f'$ is continuous on $[a,b]$
125910
Continuity of Integration for a measurable function
149354
Proof of continuity $f(x+y) = f(x) + f(y)$
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 $f(x)$
96286
Proving that sum of two measurable functions is measurable.
94109
$f$ a real, continuous function, is it measurable?
28289
Show that $Kf(x,y)=\int_0^1k(x,y) f(y) \,dy\\$ is linear and continuous
74364
Show that function $f$ has a continuous extension to $[a,b]$ iff $f$ is uniformly continuous on $(a,b)$
122160
$f:\mathbb R \to \mathbb R$ be a continuous such that $f(f(f(x)))=x,\forall x \in \mathbb R$ , is $f(x)=x , \forall x \in \mathbb R$?
86327
If the absolute value of a function is continuous, is the function continuous?
146707
Formally show that the set of continuous functions is not measurable