How to show that $f_n(x) \to f$ pointwise?
60282
Prove that $f_n$ converges uniformly on $\mathbb{R}$
127538
Show $f(x)=x\ln x$ is not uniformly continuous
28191
How to show that a set of discontinuous points of an increasing function is at most countable
94066
Prove that: {$f_n$} converges unifromly to $f$ on $E$ as $n \rightarrow \infty$ if and only if $\lim_{n\rightarrow \infty} ||f_n-f||_u = 0$
125723
Proof of $Y=F_X(X)$ being uniformly distributed on $[0,1]$ for arbitrary continuous $F_X$
151936
Pointwise Convergence and Convergence in the mean of Riemann-integrable functions
59724
Proving that $x_n\to L$ implies $|x_n|\to |L|$, and what about the converse?
33050
proof that translation of a function converges to function in $L^1$
128975
Behavior of $\|f\|_p$ when $p$ is near the endpoint of $I$
150896
Show that $\lim_{p \to \infty} \| f \|_p = \| f \|_\infty$
1014
Pointwise limit of continuous functions not Riemann integrable
93637
Does this sequence converge pointwise and/or in $L^1$?
145573
How to show that $f$ is a zero function?
41482
$f_n → f$ uniformly on $S$ and each $f_n$ is cont on $S$. Let $(x_n)$ be a sequence of points in $S$ converging to $x \in S$. Then $f_n(x_n) → f(x)$.
28399
Showing $f$ is constant
5229
Prove that $\lim_{n \to \infty} \int_0^1{nx^nf(x)}dx$ is equal to $f(1)$.
150770
Why is $f^n(\xi(x))$ continuous over $x$?