List questions from real-analysis

Published on 11 May 2026 - 5:10

569

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Sobolev inequality as a consequence of the Hardy-Littlewood-Sobolev inequality

Published on 14 Apr 2026 - 2:01

210

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Does there exist a continuous function $f: \mathbb{R} \to \mathbb{R}$ that takes each value in $\mathbb{R}$ exactly two times?

Published on 13 Apr 2026 - 23:58

175

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Computing the limit of two sequences via Monotone convergence theorem.

Published on 23 Apr 2026 - 6:27

66

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Show convergence of a series involving power series

Published on 12 Apr 2026 - 20:29

369

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Infinite divisibility of random variables

Published on 12 Apr 2026 - 16:48

25.2k

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Product rule for gradient

Published on 11 May 2026 - 8:20

66

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Is this set is complete?

Published on 13 May 2026 - 7:48

350

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Is there a rigorous way to define uncountable products?

Published on 10 May 2026 - 13:48

83

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Explain why the function $ \ f: [-\pi, \pi] \times [-\pi,\pi] \to \mathbb{R}^3 \ $ is continuous

Published on 12 Apr 2026 - 7:59

64

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How to apply theorems to answer calculus problems

Published on 06 May 2026 - 5:10

46

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Proof Verification/Help: Convergence of sequence

Published on 10 May 2026 - 15:50

100

Views

Prove $\lambda(G)=1/(a-1)$ where $G=\{(x,y)|1<x \wedge 0<y<x^{-a} \}$ with $a>1$

Published on 11 May 2026 - 7:23

35

Views

Inequalities in definitions of convergence?

Published on 11 May 2026 - 2:20

611

Views

$f$ be a continuous function maps Cauchy into Cauchy. Is $f$ uniformly continuous?

Published on 10 May 2026 - 14:04

List Question

Bernouilli inequality for exponential sequence

Sobolev inequality as a consequence of the Hardy-Littlewood-Sobolev inequality

Does there exist a continuous function $f: \mathbb{R} \to \mathbb{R}$ that takes each value in $\mathbb{R}$ exactly two times?

Computing the limit of two sequences via Monotone convergence theorem.

Show convergence of a series involving power series

Infinite divisibility of random variables

Product rule for gradient

Is this set is complete?

Is there a rigorous way to define uncountable products?

Explain why the function $ \ f: [-\pi, \pi] \times [-\pi,\pi] \to \mathbb{R}^3 \ $ is continuous

How to apply theorems to answer calculus problems

Proof Verification/Help: Convergence of sequence

Prove $\lambda(G)=1/(a-1)$ where $G=\{(x,y)|1<x \wedge 0<y<x^{-a} \}$ with $a>1$

Inequalities in definitions of convergence?

$f$ be a continuous function maps Cauchy into Cauchy. Is $f$ uniformly continuous?

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