Showing that the event: $X$ is continuous on $[0,t_0)$ belongs to the given filtration.
65334
Show that a certain set is measurable
144614
If $f$ is continuous on $[a,b]$ and $F(x) = \sup f([a,x])$. Prove that $F$ is continuous on $[a,b]$ .
125723
Proof of $Y=F_X(X)$ being uniformly distributed on $[0,1]$ for arbitrary continuous $F_X$
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
94781
Prove that $M(t)=\sup_ {a \leq x \leq t} f(x)$ given $f(x)$ is continuous on $[a,b]$
75137
proving that $f(x) = x^s$ is holder continuous with holder exponent s
111907
Prove that Cantor function is Hölder continuous
113687
$f$ is continuous function from $ [0,1]$ to itself and f(0)=0, f(1)=1 and $f(f(x))=x$ then show that $f(x)=x$ on$[0,1]$
87239
Prove functions defined by sup and inf are continuous
150770
Why is $f^n(\xi(x))$ continuous over $x$?
143174
property of continuous function
23436
$f$ Holder continuous with Holder exponent $p>1\implies f \text{ is constant}$
100187
Show function is continuous at origin
65346
Characterisation of uniformly continuous function
53627
Proving continuity of $f$
12523
Supremum of a Continuous Function is Continuous
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 $x$