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A few questions regarding using Markov/Chebyshev and writing the Lebesgue measure in terms of the Lebesgue Integral

score 79 · Answer 1 · 2026-04-10 16:12:10

79

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A few questions regarding using Markov/Chebyshev and writing the Lebesgue measure in terms of the Lebesgue Integral

Published on 10 Apr 2026 - 16:12

score 78 · Answer 2 · 2026-04-12 09:14:22

78

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Is this a reasonable measure for comparing the sizes of two sets of real numbers?

Published on 12 Apr 2026 - 9:14

score 410 · Answer 3 · 2026-04-11 16:57:33

410

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Help with finding the Lebesgue decomposition of measures

Published on 11 Apr 2026 - 16:57

score 355 · Answer 4 · 2026-03-29 00:00:02

355

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What is the Lebesgue measure of the Koch and the Minkowski curves?

Published on 29 Mar 2026 - 0:00

score 748 · Answer 5 · 2026-04-17 15:10:38

748

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$\rho(f,g)=\int_E \min(1,|f-g|)dm$. Prove that $f_n$ converges to $f$ in measure if and only if $\rho(f_n,f)\rightarrow 0$ as $n\rightarrow\infty$

Published on 17 Apr 2026 - 15:10

score 49 · Answer 6 · 2026-04-16 09:34:12

49

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Show that $\int_0^1\frac{1}{|f(x)-x_0|}dx$ is unbounded

Published on 16 Apr 2026 - 9:34

score 68 · Answer 7 · 2026-04-10 16:31:44

68

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Lebesgue measure on $\mathbb{R}^2$

Published on 10 Apr 2026 - 16:31

score 75 · Answer 8 · 2026-04-15 17:11:50

75

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Integral non-zero only if integrand is to the power of two

Published on 15 Apr 2026 - 17:11

score 50 · Answer 9 · 2026-04-17 05:06:22

50

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Is it necessarily true that $\int_0^1\frac{1}{(x+f_n(x))\log(n+1)}dx\rightarrow0$ as $n\rightarrow\infty$ under these conditions

Published on 17 Apr 2026 - 5:06

score 91 · Answer 10 · 2026-04-15 20:23:55

91

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Prove that $\lim_{j\rightarrow\infty}\int_1^\infty\frac{f_j(x)}{x}dx=\int_1^\infty\frac{f(x)}{x}dx$ under these conditions...

Published on 15 Apr 2026 - 20:23

score 373 · Answer 11 · 2026-04-16 10:06:26

373

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Given $f$ is a Lebesgue measurable function and $\int_0^1 x^{2n}f = 0 ~~~ \forall n$ , then show that $f = 0$ a.e.

Published on 16 Apr 2026 - 10:06

score 55 · Answer 12 · 2026-04-16 06:38:05

55

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Show $0<\epsilon<1$ there exists some $\delta_{p,\epsilon}>0$ such that $m(\{x\in X:|f(x)|>\epsilon\})\geq\delta_{p,\epsilon}$ for each $f\in E_p$.

Published on 16 Apr 2026 - 6:38

score 26 · Answer 13 · 2026-04-15 03:47:53

26

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Evaluate the induced measure $mT^{-1}(A)$ of the set $A$ in the following cases.

Published on 15 Apr 2026 - 3:47

score 79 · Answer 14 · 2026-04-14 04:54:02

79

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Lebesgue measure and Left and right inverse distribution functions

Published on 14 Apr 2026 - 4:54

score 143 · Answer 15 · 2026-04-09 03:39:13

143

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A question about finding Lebesgue measure of a specific set I am unable to find

Published on 09 Apr 2026 - 3:39

List Question

A few questions regarding using Markov/Chebyshev and writing the Lebesgue measure in terms of the Lebesgue Integral

Is this a reasonable measure for comparing the sizes of two sets of real numbers?

Help with finding the Lebesgue decomposition of measures

What is the Lebesgue measure of the Koch and the Minkowski curves?

$\rho(f,g)=\int_E \min(1,|f-g|)dm$. Prove that $f_n$ converges to $f$ in measure if and only if $\rho(f_n,f)\rightarrow 0$ as $n\rightarrow\infty$

Show that $\int_0^1\frac{1}{|f(x)-x_0|}dx$ is unbounded

Lebesgue measure on $\mathbb{R}^2$

Integral non-zero only if integrand is to the power of two

Is it necessarily true that $\int_0^1\frac{1}{(x+f_n(x))\log(n+1)}dx\rightarrow0$ as $n\rightarrow\infty$ under these conditions

Prove that $\lim_{j\rightarrow\infty}\int_1^\infty\frac{f_j(x)}{x}dx=\int_1^\infty\frac{f(x)}{x}dx$ under these conditions...

Given $f$ is a Lebesgue measurable function and $\int_0^1 x^{2n}f = 0 ~~~ \forall n$ , then show that $f = 0$ a.e.

Show $0<\epsilon<1$ there exists some $\delta_{p,\epsilon}>0$ such that $m(\{x\in X:|f(x)|>\epsilon\})\geq\delta_{p,\epsilon}$ for each $f\in E_p$.

Evaluate the induced measure $mT^{-1}(A)$ of the set $A$ in the following cases.

Lebesgue measure and Left and right inverse distribution functions

A question about finding Lebesgue measure of a specific set I am unable to find

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