Question

Show that $\lim_{n\to \infty} \int_E \cos^2(nx + a_n) dx = \frac{1}{2}m(E)$

score 342 · Answer 1 · 2026-04-15 18:33:57

342

Views

Show that $\lim_{n\to \infty} \int_E \cos^2(nx + a_n) dx = \frac{1}{2}m(E)$

Published on 15 Apr 2026 - 18:33

score 56 · Answer 2 · 2026-04-15 04:10:50

56

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When this series converges?

Published on 15 Apr 2026 - 4:10

score 92 · Answer 3 · 2026-04-14 13:07:21

92

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How do I conclude from $ f \notin L^{p}$ that $f_{n} \nrightarrow f$ in $L^{p}$

Published on 14 Apr 2026 - 13:07

score 93 · Answer 4 · 2026-04-13 12:04:53

93

Views

Leibniz convergence test to compute the limit

Published on 13 Apr 2026 - 12:04

score 81 · Answer 5 · 2026-04-11 13:37:08

81

Views

Uniform convergence of the following series:

Published on 11 Apr 2026 - 13:37

score 176 · Answer 6 · 2026-04-15 10:57:51

176

Views

Beef with solution to showing sequence $\{s_n\}$ converges where $s_{n+1} = \sqrt{2 + \sqrt{s_n}}$

Published on 15 Apr 2026 - 10:57

score 499 · Answer 7 · 2026-04-10 19:10:50

499

Views

Application of Lévy Zero-One Law

Published on 10 Apr 2026 - 19:10

score 44 · Answer 8 · 2026-04-16 10:00:12

44

Views

If $Y_n=E(X|\mathcal{F}_n)$ for some $\mathcal{F}_n \subset \mathcal{F}$ and if $Y_n \to Y$ with probability one. Show $Y_n \to Y$ in $L^1$.

Published on 16 Apr 2026 - 10:00

score 85 · Answer 9 · 2026-04-16 04:58:36

85

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Radius of convergence of $\sum_{n=1}^\infty (-1)^n\;n\;4^n\;x^n$

Published on 16 Apr 2026 - 4:58

score 1.6k · Answer 10 · 2026-04-16 01:46:00

1.6k

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Series $\sum_{n=1}^{\infty} \frac{n^2 - 5n}{n^3 + n + 1}$

Published on 16 Apr 2026 - 1:46

score 131 · Answer 11 · 2026-03-25 04:36:26

131

Views

Understanding the roots in the Weierstrass factorization theorem

Published on 25 Mar 2026 - 4:36

score 30 · Answer 12 · 2026-04-15 22:07:11

30

Views

How does the inequality $|\hat V_1-V|\le \max_{1\le i\le n}\Big|\frac{1}{1+\tilde\lambda g_i}\Big|^2\cdot|\frac1n\sum_{i=1}^ng_i^2- V|$ hold?

Published on 15 Apr 2026 - 22:07

score 3.1k · Answer 13 · 2026-04-13 08:34:54

3.1k

Views

Why are the sums of absolutely convergent series not affected by changing the order of summation?

Published on 13 Apr 2026 - 8:34

score 109 · Answer 14 · 2026-04-13 03:22:14

109

Views

Weak convergence in $\ell_p$

Published on 13 Apr 2026 - 3:22

score 53 · Answer 15 · 2026-04-15 20:17:02

53

Views

Are $\sum\frac{1}{\sqrt{n(n+1)}},\sum\frac{1}{\sqrt{n(n^2+1)}}$ convergent or divergent?

Published on 15 Apr 2026 - 20:17

List Question

Show that $\lim_{n\to \infty} \int_E \cos^2(nx + a_n) dx = \frac{1}{2}m(E)$

When this series converges?

How do I conclude from $ f \notin L^{p}$ that $f_{n} \nrightarrow f$ in $L^{p}$

Leibniz convergence test to compute the limit

Uniform convergence of the following series:

Beef with solution to showing sequence $\{s_n\}$ converges where $s_{n+1} = \sqrt{2 + \sqrt{s_n}}$

Application of Lévy Zero-One Law

If $Y_n=E(X|\mathcal{F}_n)$ for some $\mathcal{F}_n \subset \mathcal{F}$ and if $Y_n \to Y$ with probability one. Show $Y_n \to Y$ in $L^1$.

Radius of convergence of $\sum_{n=1}^\infty (-1)^n\;n\;4^n\;x^n$

Series $\sum_{n=1}^{\infty} \frac{n^2 - 5n}{n^3 + n + 1}$

Understanding the roots in the Weierstrass factorization theorem

How does the inequality $|\hat V_1-V|\le \max_{1\le i\le n}\Big|\frac{1}{1+\tilde\lambda g_i}\Big|^2\cdot|\frac1n\sum_{i=1}^ng_i^2- V|$ hold?

Why are the sums of absolutely convergent series not affected by changing the order of summation?

Weak convergence in $\ell_p$

Are $\sum\frac{1}{\sqrt{n(n+1)}},\sum\frac{1}{\sqrt{n(n^2+1)}}$ convergent or divergent?

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