Show that the set of points $x$ where $(f_{n}(x))$ is convergent is a Borel subset of $\mathbb{R}$
68143
The set of convergent points of a sequence of continuous functions is Borel
147429
Set of points in $\mathbb{C}$ s.t. $z^{n-1} = \overline z$
18222
Set of continuity points of a real function
88610
The set of convergence of a sequence of measurable functions is measurable
156922
Proving convergence iff projection converges in product topology
94066
Prove that: {$f_n$} converges unifromly to $f$ on $E$ as $n \rightarrow \infty$ if and only if $\lim_{n\rightarrow \infty} ||f_n-f||_u = 0$
76593
Show that $f_n(z)=z^n$ converges locally uniformly on $|z|<1$ but not uniformly(?)
156905
Prove $f_n$ has a uniformly convergent subsequence on $[0,1]$.
50137
Using Cantor's lemma in a proof of convergence
133707
Notions of strong and weak convergence for $L^{2}(\mathbb R, \lambda)$ where $f_{n}(x)=1_{[n,n+1]}(x)$
28191
How to show that a set of discontinuous points of an increasing function is at most countable
59424
Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
102756
What are the subsets of the unit circle that can be the points in which a power series is convergent?
85285
Show $\sum_{i=1}^\infty x_i y_i$ is absolutely convergent
117649
$f:[0,1]\to[0,1]$ be a continuous function. Let $x_1\in[0,1]$ and define $x_{n+1}={\sum_{i=1}^n f(x_i)\over n}$.Prove, $\{x_n\}$ is convergent
35535
Sequence of sets $f_n$ that converge almost everywhere to $f$ but not almost uniformly to $f$?
157384
Points of continuity is a Borel set?