List questions from lebesgue-integral

Published on 06 Oct 2018 - 7:21

130

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If $(f_j)\to f$ in measure, show that $\int_X f\,d\mu\le\varliminf\int_X f_j\,d\mu$

Published on 06 Oct 2018 - 16:59

77

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$f = g$ a.e. implies $\int_{A}f\,d\mu = \int_{A}g\,d\mu$

Published on 07 Oct 2018 - 7:15

107

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intuitively obvious integration identity

Published on 07 Oct 2018 - 13:57

106

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Integral list w. r. t. measure?

Published on 07 Oct 2018 - 22:13

227

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Application of the the Dominated Convergence Theorem

Published on 09 Oct 2018 - 0:15

236

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Measure theory and integration textbook

Published on 26 Mar 2026 - 12:34

36

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limsup in an integral inequality

Published on 09 Oct 2018 - 8:25

263

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Lebesgue integrability if xf(x) is integrable in R+

Published on 10 Oct 2018 - 17:56

175

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Strongly convergent subsequence $+$ point-wise convergence $\Rightarrow$ strong convergence?

Published on 22 Mar 2026 - 13:26

39

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Clarification on a proof of Fatou's Lemma

Published on 10 Oct 2018 - 19:40

106

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How does countable additivity imply convergence in Rudin's theorem 11.3?

Published on 11 Oct 2018 - 22:35

594

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Sobolev-function $u\in W^{1, p}(\mathbb{R}^n)$ which is unbounded on every open set $U\subset\mathbb{R}^n$

Published on 13 Oct 2018 - 7:50

67

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Completetion of Measure in the Definition of Functions

Published on 13 Oct 2018 - 22:42

91

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Partition of a lower and upper sum in Riemann Integration.

Published on 26 Mar 2026 - 14:20

List Question

Dominated convergence with variable limit

If $(f_j)\to f$ in measure, show that $\int_X f\,d\mu\le\varliminf\int_X f_j\,d\mu$

$f = g$ a.e. implies $\int_{A}f\,d\mu = \int_{A}g\,d\mu$

intuitively obvious integration identity

Integral list w. r. t. measure?

Application of the the Dominated Convergence Theorem

Measure theory and integration textbook

limsup in an integral inequality

Lebesgue integrability if xf(x) is integrable in R+

Strongly convergent subsequence $+$ point-wise convergence $\Rightarrow$ strong convergence?

Clarification on a proof of Fatou's Lemma

How does countable additivity imply convergence in Rudin's theorem 11.3?

Sobolev-function $u\in W^{1, p}(\mathbb{R}^n)$ which is unbounded on every open set $U\subset\mathbb{R}^n$

Completetion of Measure in the Definition of Functions

Partition of a lower and upper sum in Riemann Integration.

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