Question

How to prove that for a compact set to be measure zero, we need $\forall \epsilon > 0$, there exists a finite covering satisfying the necessary condn

score 569 · Answer 1 · 2026-04-13 18:55:10

569

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How to prove that for a compact set to be measure zero, we need $\forall \epsilon > 0$, there exists a finite covering satisfying the necessary condn

Published on 13 Apr 2026 - 18:55

score 806 · Answer 2 · 2026-04-16 22:28:40

806

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Let $P'$ be a refinement of the partition $P$, then $s(f,P) \leq s(f,P') \leq S(f,P') \leq S(f,P)$

Published on 16 Apr 2026 - 22:28

score 62 · Answer 3 · 2026-04-15 10:41:48

62

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A condition for independence of two random variables and a counterexample

Published on 15 Apr 2026 - 10:41

score 246 · Answer 4 · 2026-04-11 23:35:41

246

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Mean value theorem on open interval

Published on 11 Apr 2026 - 23:35

score 618 · Answer 5 · 2026-04-10 22:27:54

618

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Counterexamples for strong laws of large numbers

Published on 10 Apr 2026 - 22:27

score 2.1k · Answer 6 · 2026-04-13 17:03:07

2.1k

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Is the sum of the series $\sum \frac{\sin nx^2}{1 + n^3}$ continuously differentiable?

Published on 13 Apr 2026 - 17:03

score 122 · Answer 7 · 2026-04-17 13:13:59

122

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Determining whether sequence $a_n=\sum_{k=1}^n\frac n{n^2+k}$ is convergent or not.

Published on 17 Apr 2026 - 13:13

score 91 · Answer 8 · 2026-04-11 09:31:26

91

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Another version of mean value theorem

Published on 11 Apr 2026 - 9:31

score 252 · Answer 9 · 2026-04-20 16:47:26

252

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Divergence of a Series $\sum_{n=1}^\infty (\frac{1}{n!})(\frac{n}{e})^n$

Published on 20 Apr 2026 - 16:47

score 1.8k · Answer 10 · 2026-04-18 06:24:29

1.8k

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What is the closed form of the sequence : $ a_{n+2} = 2a_{n+1}-a_n+2^n+2 $

Published on 18 Apr 2026 - 6:24

score 133 · Answer 11 · 2026-04-16 18:42:48

133

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Calculate $\int\int_E e^{5x^2+2xy+y^2}dA$

Published on 16 Apr 2026 - 18:42

score 32 · Answer 12 · 2026-04-10 12:22:00

32

Views

Distribution function constraints from moments?

Published on 10 Apr 2026 - 12:22

score 208 · Answer 13 · 2026-04-20 05:06:13

208

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Find the closed form of $u_{n+1}=a_nu_n+b_n$

Published on 20 Apr 2026 - 5:06

score 91 · Answer 14 · 2026-04-17 20:23:01

If $f:[0, \pi] \rightarrow \mathbb{R}$ is continuous, $f(0) = 0$, then does $\int_0^\pi f(t)\cos nt\,dt = 0$ for $n=0, 1,2,\dots$ imply $f = 0$?

score 85 · Answer 15 · 2026-04-06 19:02:14

85

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If $f$ and $g$ are bounded on $[a,b]$, prove that $\rVert f+g \lVert_u \leq \lVert f \rVert_u + \lVert g \rVert_u$

Published on 06 Apr 2026 - 19:02

List Question

How to prove that for a compact set to be measure zero, we need $\forall \epsilon > 0$, there exists a finite covering satisfying the necessary condn

Let $P'$ be a refinement of the partition $P$, then $s(f,P) \leq s(f,P') \leq S(f,P') \leq S(f,P)$

A condition for independence of two random variables and a counterexample

Mean value theorem on open interval

Counterexamples for strong laws of large numbers

Is the sum of the series $\sum \frac{\sin nx^2}{1 + n^3}$ continuously differentiable?

Determining whether sequence $a_n=\sum_{k=1}^n\frac n{n^2+k}$ is convergent or not.

Another version of mean value theorem

Divergence of a Series $\sum_{n=1}^\infty (\frac{1}{n!})(\frac{n}{e})^n$

What is the closed form of the sequence : $ a_{n+2} = 2a_{n+1}-a_n+2^n+2 $

Calculate $\int\int_E e^{5x^2+2xy+y^2}dA$

Distribution function constraints from moments?

Find the closed form of $u_{n+1}=a_nu_n+b_n$

If $f:[0, \pi] \rightarrow \mathbb{R}$ is continuous, $f(0) = 0$, then does $\int_0^\pi f(t)\cos nt\,dt = 0$ for $n=0, 1,2,\dots$ imply $f = 0$?

If $f$ and $g$ are bounded on $[a,b]$, prove that $\rVert f+g \lVert_u \leq \lVert f \rVert_u + \lVert g \rVert_u$

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