List questions from lebesgue-integral

63

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Let $f \in L^2[0,\infty)$ be a continuous, positive and decreasing function, then $\lim_{x\to \infty}\sqrt{x}f(x)=0$

Published on 25 Apr 2020 - 2:34

502

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Lebesgue Integral - Self Learning

Published on 31 Mar 2026 - 19:08

412

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Average squared distance between two points on a disk

Published on 25 Apr 2020 - 16:51

109

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Is, "$|f_n|\leq g$ eventually", sufficient for dominated convergence theorem

Published on 25 Apr 2020 - 21:47

17

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$0<C<1$, show $\exists \delta_n \to 0$ s.t if $A_k, 1\leq k\leq n$ and $\lambda(A_k)=C$ then $\lambda(A_i\cap A_j)\geq(1-\delta_n)C^2$ for some $i,j$

Published on 25 Apr 2020 - 23:34

23

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Show that $\chi_{[0,t]}$ is not differentiable in $L^1$ norm.

Published on 26 Apr 2020 - 1:27

44

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Let $f \in C^1(\mathbb{R})$ and $f\in L^1([0,\infty))$ compute limits, reminiscent of Riemann-Lebesgue lemma

Published on 26 Apr 2020 - 3:31

34

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Mixed $L^p \ell^q$ -norm Minkowski type inequality?

Published on 26 Apr 2020 - 19:48

189

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Condition for $L^r(\mu)=L^\infty(\mu)$ where $\mu(X)=1$

Published on 28 Mar 2026 - 23:58

96

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Equality of Riemann and Lebesgue integrals

Published on 27 Apr 2020 - 1:23

119

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Convergence in measure, a few questions.

Published on 27 Apr 2020 - 3:26

91

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Counterexample for Finding Lebesgue Integrable Function

Published on 27 Apr 2020 - 7:14

59

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Computation of integral on set determined by orbits

Published on 28 Mar 2026 - 6:21

201

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Prove that $F\in L^1(\mathbb{R})$

Published on 01 Apr 2026 - 17:12

179

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Proposition 4 of Chapter $4$ From Royden Real Analysis

Published on 30 Mar 2026 - 6:18

List Question

Let $f \in L^2[0,\infty)$ be a continuous, positive and decreasing function, then $\lim_{x\to \infty}\sqrt{x}f(x)=0$

Lebesgue Integral - Self Learning

Average squared distance between two points on a disk

Is, "$|f_n|\leq g$ eventually", sufficient for dominated convergence theorem

$0<C<1$, show $\exists \delta_n \to 0$ s.t if $A_k, 1\leq k\leq n$ and $\lambda(A_k)=C$ then $\lambda(A_i\cap A_j)\geq(1-\delta_n)C^2$ for some $i,j$

Show that $\chi_{[0,t]}$ is not differentiable in $L^1$ norm.

Let $f \in C^1(\mathbb{R})$ and $f\in L^1([0,\infty))$ compute limits, reminiscent of Riemann-Lebesgue lemma

Mixed $L^p \ell^q$ -norm Minkowski type inequality?

Condition for $L^r(\mu)=L^\infty(\mu)$ where $\mu(X)=1$

Equality of Riemann and Lebesgue integrals

Convergence in measure, a few questions.

Counterexample for Finding Lebesgue Integrable Function

Computation of integral on set determined by orbits

Prove that $F\in L^1(\mathbb{R})$

Proposition 4 of Chapter $4$ From Royden Real Analysis

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