Weak convergence + compactness = strong convergence?
2471
Every subsequence of $x_n$ has a further subsequence which converges to $x$. Then the sequence $x_n$ converges to $x$.
41057
Does $L^p$-convergence imply pointwise convergence for $C_0^\infty$ functions?
79496
Holomorphic functions which converge pointwise but not almost uniformly
9268
Proving that the Union of Two Compact Sets is Compact
11558
How to show that the limit of compact operators in the operator norm topology is compact
67006
Sequence of functions: Convergence
119558
A basic question on convergence in prob. and a.s. convergence
117764
Almost surely convergence of the sequence
122911
Characterization of weak convergence in $\ell_\infty$
134136
Does weak convergence imply $L^2$-norm convergence?
148302
In convergence, why not $d \leq \epsilon$?
45249
Pseudocompactness does not imply compactness
60282
Prove that $f_n$ converges uniformly on $\mathbb{R}$
155822
Does uniform convergence preserves absolute continuity?
148349
Uniform convergence with two sequences of functions
41208
weak convergence in $L^p$ plus convergence of norm implies strong convergence
35514
If $\{f_n\}$ converges uniformly and each $f_n$ is bounded, show that $\exists M>0$ s.t. $|f_n(x)| \leq M$