List questions from lebesgue-integral

Published on 25 Mar 2026 - 17:17

88

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Multiplication of simple function looks like?

Published on 25 Mar 2026 - 1:15

46

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Give an example function $f \in L_p(\mathbb {R}) \forall \: p > 7,$ but $f \notin L_p(\mathbb {R}) \: p \leq 7$

Published on 23 May 2020 - 15:14

97

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Deep doubt on a double surface integral

Published on 28 Mar 2026 - 8:47

668

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Measure theory: motivation behind monotone convergence theorem

Published on 23 May 2020 - 23:37

941

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For (Lebesgue) measurable functions $f$ and $g$, if $f=g$ a.e., then $ \int_{E} f=\int_{E} g. $

Published on 24 May 2020 - 14:39

208

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For $g(x) = 1/x$ extended to complex-values, what is antiderivative of $g$?

Published on 29 Mar 2026 - 3:28

97

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Simple Change of Variables in Lebesgue Integration

Published on 26 Mar 2026 - 23:09

479

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Prove that $f\in L^1(A)\Leftrightarrow \sum_{n}^{\infty}m(\{ x\in A : f(x)\geq n \}) < \infty$

Published on 25 Mar 2026 - 8:10

57

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Convergence of integral by using a Lebesgue point

Published on 25 May 2020 - 10:11

84

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$f(x)=1/(|x|+1)^k$ defined on $\Bbb R^k$ is not integrable

Published on 25 May 2020 - 13:55

639

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Monotonicity of the Lebesgue Integral

Published on 25 May 2020 - 18:55

198

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Set of lower dimension has Lebesgue measure zero?

Published on 25 May 2020 - 19:08

32

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Is this version of the dominated convergence theorem true?

Published on 26 May 2020 - 9:13

77

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Lebesgue integral, Is the solution right?

Published on 26 May 2020 - 9:52

List Question

a.e-defined integrable functions

Multiplication of simple function looks like?

Give an example function $f \in L_p(\mathbb {R}) \forall \: p > 7,$ but $f \notin L_p(\mathbb {R}) \: p \leq 7$

Deep doubt on a double surface integral

Measure theory: motivation behind monotone convergence theorem

For (Lebesgue) measurable functions $f$ and $g$, if $f=g$ a.e., then $ \int_{E} f=\int_{E} g. $

For $g(x) = 1/x$ extended to complex-values, what is antiderivative of $g$?

Simple Change of Variables in Lebesgue Integration

Prove that $f\in L^1(A)\Leftrightarrow \sum_{n}^{\infty}m(\{ x\in A : f(x)\geq n \}) < \infty$

Convergence of integral by using a Lebesgue point

$f(x)=1/(|x|+1)^k$ defined on $\Bbb R^k$ is not integrable

Monotonicity of the Lebesgue Integral

Set of lower dimension has Lebesgue measure zero?

Is this version of the dominated convergence theorem true?

Lebesgue integral, Is the solution right?

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