New posts in weak-convergence

Why $\sin(nx)$ converges weakly in $L^2(-\pi,\pi)$?

Convergence in probability implies convergence in distribution

Weak convergence, together with convergence of norms, implies strong convergence in a Hilbert space.

Characterization of weak convergence in $\ell_\infty$

A question involving Lindeberg-Levy CLT

Does weak convergence in $L^2$ implies convergence almost everywhere along subsequence?

Weak convergence in probability implies uniform convergence in distribution functions

Schur's Theorem: In $\ell^1$ weak convergence of $x_n$ is the same as convergence in the norm

$\ell_\infty$ is a Grothendieck space

Pointwise a.e. convergence and weak convergence in Lp

Weak convergence in $L^p$ space

An example of distributional limit

Weak convergence of a sequence $(f_n) \subset L^2(\mathbb{R})$ and convergence of $\chi_n f_n$

Proving the closed unit ball of a Hilbert space is weakly sequentially compact

Every bounded sequence has a weakly convergent subsequence in a Hilbert space

Rate of Weak Convergence for a Sequence of Probability Measures

Is the weak topology sequential on some infinite-dimensional Banach space?

Understanding weakly dense.

Portmanteau theorem for vague convergence

Strong and weak convergence in $\ell^1$