List questions from lebesgue-integral

Published on 24 Feb 2026 - 2:11

35

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Inequality involving the measure of $\displaystyle\limsup_{n\to\infty}(\{x\in{}X:|f_n(x)|\geq{}a/2\})$

Published on 01 Feb 2020 - 20:41

68

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Dominated convergence theorem on Lebesgue's integral

Published on 02 Feb 2020 - 13:02

41

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Does $f_n\to{}0$ and $\int_{[0,1]}f_nd\mu=1$ for every $n\geq{}1$ imply $\int_{[0,1]}\displaystyle\sup_{n}f_nd\mu=\infty$?

Published on 02 Feb 2020 - 13:27

100

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Measurability of intermediate variable in the application of the mean-value theorem

Published on 02 Feb 2020 - 13:50

58

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pointwise convergence of sequence of function

Published on 24 Feb 2026 - 2:11

60

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Does $f(x + n)$ go to zero for almost all $x \in \mathbb{R}$ and $f$ integrable.

Published on 03 Feb 2020 - 14:42

40

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$\int_D X dP = 0$ for all $D\in \mathcal A \cup\mathcal B \implies \int_D X d P = 0$ for all $D\in \sigma[\mathcal A \cup \mathcal B]$?

Published on 05 Feb 2020 - 5:15

49

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Cauchy Principal Value - nomenclature question

Published on 25 Mar 2026 - 11:10

628

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f bounded and measurable implies L-integrable?

Published on 07 Feb 2020 - 12:03

115

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Is $f$ also necessarily of bounded variation?

Published on 26 Mar 2026 - 11:04

179

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Rudin Real and Complex Analysis, How Theorem 7.10 leads to a generalization of Theorem 7.8?

Published on 10 Feb 2020 - 7:56

501

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Conditional Expectation as Almost Sure Convergence

Published on 01 Apr 2026 - 23:27

120

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Density of $C^\infty_0$ in a certain weighted $L^2$ space on the line

Published on 11 Feb 2020 - 1:01

84

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Locally integrable function in Lebesgue sense

Published on 29 Mar 2026 - 18:12

List Question

On convergence and Lebesgue Integration

Inequality involving the measure of $\displaystyle\limsup_{n\to\infty}(\{x\in{}X:|f_n(x)|\geq{}a/2\})$

Dominated convergence theorem on Lebesgue's integral

Does $f_n\to{}0$ and $\int_{[0,1]}f_nd\mu=1$ for every $n\geq{}1$ imply $\int_{[0,1]}\displaystyle\sup_{n}f_nd\mu=\infty$?

Measurability of intermediate variable in the application of the mean-value theorem

pointwise convergence of sequence of function

Does $f(x + n)$ go to zero for almost all $x \in \mathbb{R}$ and $f$ integrable.

$\int_D X dP = 0$ for all $D\in \mathcal A \cup\mathcal B \implies \int_D X d P = 0$ for all $D\in \sigma[\mathcal A \cup \mathcal B]$?

Cauchy Principal Value - nomenclature question

f bounded and measurable implies L-integrable?

Is $f$ also necessarily of bounded variation?

Rudin Real and Complex Analysis, How Theorem 7.10 leads to a generalization of Theorem 7.8?

Conditional Expectation as Almost Sure Convergence

Density of $C^\infty_0$ in a certain weighted $L^2$ space on the line

Locally integrable function in Lebesgue sense

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