List questions from lebesgue-integral

Published on 30 Mar 2026 - 5:12

61

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$\int f\,d\mu<\infty\Leftrightarrow\sum_{n=0}^\infty\frac{1}{2^n}\mu\left(\left\{x\in X:f(x)\geq\frac{1}{2^n}\right\}\right)<\infty$

Published on 28 Mar 2026 - 22:29

590

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"Take Expectation of Both Sides" via Lebesgue Integration?

Published on 06 Apr 2020 - 15:29

708

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Prove Probability of Two Continuous Random Variables Equal is 0?

Published on 06 Apr 2020 - 18:28

19

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Relationship involving Lebesgue integral of supremum of function depending on a parameter

Published on 07 Apr 2020 - 1:37

275

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Integration with respect to measures

Published on 07 Apr 2020 - 15:36

188

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For $f\in L^1(\mathbb{R})$, show that $\lim_{\varepsilon \to 0}\int_{-\infty}^\infty \cos(\varepsilon x)f(x) \, dx=\int_{-\infty}^\infty f(x)\,dx$

Published on 07 Apr 2020 - 18:24

86

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Question on Upper Functions and Lebesgue Integral

Published on 08 Apr 2020 - 3:32

102

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Show that $Mf_n(x) \nearrow Mf(x)$, where $f_n(x) \nearrow f(x)$ almost everywhere

Published on 28 Mar 2026 - 7:41

148

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How is this "differential" element converted from a geometric/pictorial form into an integral?

Published on 30 Mar 2026 - 3:02

2.3k

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Is the product of $L^1$ functions $L^1$?

Published on 09 Apr 2020 - 8:02

45

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Are most functions measurable?

Published on 28 Mar 2026 - 23:57

36

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bounded convergence theorem is not holding

Published on 09 Apr 2020 - 17:00

45

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$g$ is Lebesgue Integrable Implies $g < \infty$ a.e. (Papa Rudin 1.41)

Published on 09 Apr 2020 - 21:43

54

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weighted integral of a continuous function

Published on 09 Apr 2020 - 22:33

List Question

Convergence in $L^1$-norm Involving Convolution

$\int f\,d\mu<\infty\Leftrightarrow\sum_{n=0}^\infty\frac{1}{2^n}\mu\left(\left\{x\in X:f(x)\geq\frac{1}{2^n}\right\}\right)<\infty$

"Take Expectation of Both Sides" via Lebesgue Integration?

Prove Probability of Two Continuous Random Variables Equal is 0?

Relationship involving Lebesgue integral of supremum of function depending on a parameter

Integration with respect to measures

For $f\in L^1(\mathbb{R})$, show that $\lim_{\varepsilon \to 0}\int_{-\infty}^\infty \cos(\varepsilon x)f(x) \, dx=\int_{-\infty}^\infty f(x)\,dx$

Question on Upper Functions and Lebesgue Integral

Show that $Mf_n(x) \nearrow Mf(x)$, where $f_n(x) \nearrow f(x)$ almost everywhere

How is this "differential" element converted from a geometric/pictorial form into an integral?

Is the product of $L^1$ functions $L^1$?

Are most functions measurable?

bounded convergence theorem is not holding

$g$ is Lebesgue Integrable Implies $g < \infty$ a.e. (Papa Rudin 1.41)

weighted integral of a continuous function

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