Question

$s + \frac{1}{n}$ is an upper bound for $A$ and $s - \frac{1}{n}$ is not an upper bound for $A$. Show $s = \sup A.$

score 1.5k · Answer 1 · 2026-04-15 19:20:04

1.5k

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$s + \frac{1}{n}$ is an upper bound for $A$ and $s - \frac{1}{n}$ is not an upper bound for $A$. Show $s = \sup A.$

Published on 15 Apr 2026 - 19:20

score 303 · Answer 2 · 2026-04-23 08:16:36

303

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uniformly convergent implies uniformly equicontinuous?

Published on 23 Apr 2026 - 8:16

score 123 · Answer 3 · 2026-04-25 08:57:07

123

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$f: [0,1]\rightarrow L^1(\Omega)$ as a (measurable?) function from $[0,1]\times \Omega\rightarrow \mathbb{R}$

Published on 25 Apr 2026 - 8:57

score 173 · Answer 4 · 2026-04-16 11:01:38

173

Views

Weierstrass M-Test: Show that the series is differentiable

Published on 16 Apr 2026 - 11:01

score 141 · Answer 5 · 2026-03-25 06:22:09

141

Views

Prove that $\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+2}+....+\frac{1}{2n}\geq \frac{2}{3}$

Published on 25 Mar 2026 - 6:22

score 1.6k · Answer 6 · 2026-04-14 19:17:01

1.6k

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Show that the set of irrational numbers is dense in $\mathbb{R}$ using definition of Closure

Published on 14 Apr 2026 - 19:17

score 57 · Answer 7 · 2026-04-24 09:35:57

57

Views

Proving this statement for improper integral

Published on 24 Apr 2026 - 9:35

score 1.3k · Answer 8 · 2026-04-15 04:49:48

Let $(f_n)$ be a sequence of monotonically increasing functions which converges pointwise to $f$ . Show that f must also be monotonically increasing

score 46 · Answer 9 · 2026-04-13 04:33:53

46

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Convergence of a sequence problem

Published on 13 Apr 2026 - 4:33

score 684 · Answer 10 · 2026-04-20 12:34:35

684

Views

For $E\subset\mathbb R^n$ with Lebesgue outer measure $0<m^(E)<\infty$, $\alpha\in(0,1)$, there is a ball $B$ with $m^(E\cap B)\ge \alpha m^*(B)$.

Published on 20 Apr 2026 - 12:34

score 205 · Answer 11 · 2026-03-24 23:51:34

205

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Prove that $f(x+y)=f(x)+f(y)$, and $f(x\cdot y) = f(x)\cdot f(y)$ implies $f:\mathbb{R} \to \mathbb{R}'$ is a bijective mapping that preserves order.

Published on 24 Mar 2026 - 23:51

score 73 · Answer 12 · 2026-04-21 15:24:57

73

Views

establish the formula $E[X]=\int_{-\infty}^{\infty} p(x)dx$

Published on 21 Apr 2026 - 15:24

score 73 · Answer 13 · 2026-04-13 17:06:41

73

Views

Sum of a series involving integral II

Published on 13 Apr 2026 - 17:06

score 538 · Answer 14 · 2026-04-12 06:45:09

538

Views

A question from the proof of the Tietze's Extension Theorem

Published on 12 Apr 2026 - 6:45

score 680 · Answer 15 · 2026-04-24 01:57:56

680

Views

Pointwise and Uniform Convergence. Showing unique limit.

Published on 24 Apr 2026 - 1:57

List Question

$s + \frac{1}{n}$ is an upper bound for $A$ and $s - \frac{1}{n}$ is not an upper bound for $A$. Show $s = \sup A.$

uniformly convergent implies uniformly equicontinuous?

$f: [0,1]\rightarrow L^1(\Omega)$ as a (measurable?) function from $[0,1]\times \Omega\rightarrow \mathbb{R}$

Weierstrass M-Test: Show that the series is differentiable

Prove that $\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+2}+....+\frac{1}{2n}\geq \frac{2}{3}$

Show that the set of irrational numbers is dense in $\mathbb{R}$ using definition of Closure

Proving this statement for improper integral

Let $(f_n)$ be a sequence of monotonically increasing functions which converges pointwise to $f$ . Show that f must also be monotonically increasing

Convergence of a sequence problem

For $E\subset\mathbb R^n$ with Lebesgue outer measure $0<m^(E)<\infty$, $\alpha\in(0,1)$, there is a ball $B$ with $m^(E\cap B)\ge \alpha m^*(B)$.

Prove that $f(x+y)=f(x)+f(y)$, and $f(x\cdot y) = f(x)\cdot f(y)$ implies $f:\mathbb{R} \to \mathbb{R}'$ is a bijective mapping that preserves order.

establish the formula $E[X]=\int_{-\infty}^{\infty} p(x)dx$

Sum of a series involving integral II

A question from the proof of the Tietze's Extension Theorem

Pointwise and Uniform Convergence. Showing unique limit.

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