List questions from weak-convergence

Published on 25 Mar 2026 - 18:59

567

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Closed convex hull of weak convergent sequence: How to show that $x$ is the only element in $\bigcap K_n$?

Published on 25 Mar 2026 - 6:29

80

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$A \in \mathcal{L}(X,Y) \implies A^* \in \mathcal{L}(Y^_{w^}, X^_{w^})$

Published on 25 Mar 2026 - 14:22

125

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Finding the weak limit of a sequence of random variables.

Published on 26 Mar 2026 - 12:58

78

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weak convergence: Show that $\mathbf{P}(X_n = q) \to 0$ as $n \to \infty$ when the cdf $F$ of the limit $X$ is continuous at $q$

Published on 25 Mar 2026 - 23:42

75

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Proving a sequence of functions converges weakly*

Published on 01 May 2019 - 13:37

483

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Weak star convergence

Published on 01 May 2019 - 16:16

121

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Weak convergence of functionals in dual space given by a sum of functionals

Published on 03 May 2019 - 12:58

57

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prove a series weakly converges to its mean value

Published on 08 May 2019 - 13:13

45

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Showing that $A(\overline{B_1^X}) \subseteq Y$ is closed when $A \in \mathcal{L}(X,Y)$.

Published on 23 Feb 2026 - 1:06

41

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Showing that $C=\{h \in L^1(\Omega) : u_1(z) \leq h(z) \leq u_2(z)\}$ is weakly compact.

Published on 25 Mar 2026 - 17:42

40

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Weak convergence of measures and boundedness

Published on 25 Mar 2026 - 23:37

114

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A question regarding Radon-Riesz property

Published on 29 Mar 2026 - 7:29

209

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A sufficient and necessary condition for a special linear operator to be compact

Published on 25 Mar 2026 - 22:10

83

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Sampling with replacement. $P[\upsilon_m>n]=\prod_{i=2}^{n}(1-\frac{i-1}{m})$.

Published on 19 May 2019 - 20:36

List Question

Example for Lévy's continuity theorem

Closed convex hull of weak convergent sequence: How to show that $x$ is the only element in $\bigcap K_n$?

$A \in \mathcal{L}(X,Y) \implies A^* \in \mathcal{L}(Y^_{w^}, X^_{w^})$

Finding the weak limit of a sequence of random variables.

weak convergence: Show that $\mathbf{P}(X_n = q) \to 0$ as $n \to \infty$ when the cdf $F$ of the limit $X$ is continuous at $q$

Proving a sequence of functions converges weakly*

Weak star convergence

Weak convergence of functionals in dual space given by a sum of functionals

prove a series weakly converges to its mean value

Showing that $A(\overline{B_1^X}) \subseteq Y$ is closed when $A \in \mathcal{L}(X,Y)$.

Showing that $C=\{h \in L^1(\Omega) : u_1(z) \leq h(z) \leq u_2(z)\}$ is weakly compact.

Weak convergence of measures and boundedness

A question regarding Radon-Riesz property

A sufficient and necessary condition for a special linear operator to be compact

Sampling with replacement. $P[\upsilon_m>n]=\prod_{i=2}^{n}(1-\frac{i-1}{m})$.

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