List questions from lebesgue-integral

Published on 08 Jan 2017 - 18:13

206

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Construct $f$ such that $f\in L^{p_0}$ but $f\notin L_p$ for $p\ne p_0$

Published on 09 Jan 2017 - 9:24

2.7k

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$fg\in L^1$ for all $g\in L^q$ $\Longrightarrow f\in L^p$

Published on 08 Apr 2026 - 4:31

58

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An inequality in $L^p$ spaces

Published on 08 Apr 2026 - 21:44

80

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$\lim_{p\rightarrow 0}\int_X|f|^p\,d\mu=\mu(\{x\in X\,|\,f(x)\ne 0\})$

Published on 08 Apr 2026 - 4:32

86

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Integral notation $\int_G d\mu(x) f(x)$

Published on 12 Jan 2017 - 11:17

76

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Does Improper Riemann integrability of type 2 mean lebesgues integrability?

Published on 31 Mar 2026 - 21:11

161

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Is the map $p\mapsto\int_X |f|^p d\mu$ differentiable when $\log|f|\notin L^1$?

Published on 08 Apr 2026 - 4:31

67

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$\int_{D} \frac{x-y}{1+x+y} d(x,y)$ for $D=\{(x,y)\in\Bbb R^{2}|0<x+y<1, 0<x-y<1\}$ using subsitution

Published on 12 Jan 2017 - 20:03

56

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Minimum of a function defined by an integral

Published on 07 Apr 2026 - 23:24

40

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Cross-sectional measures of a set of positive measure

Published on 13 Jan 2017 - 17:07

202

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Standard notation or name for the measure defined by an integral over a function

Published on 13 Jan 2017 - 22:46

46

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Is this measurability arguement correct?

Published on 14 Jan 2017 - 0:02

315

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If a set has positive measure, do its slices have positive measure?

Published on 14 Jan 2017 - 3:39

72

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Measure theory proof review: extended real valued maesurable functions with the same integral

Published on 16 Jan 2017 - 11:54

List Question

Calculate threedimensional integral of area

Construct $f$ such that $f\in L^{p_0}$ but $f\notin L_p$ for $p\ne p_0$

$fg\in L^1$ for all $g\in L^q$ $\Longrightarrow f\in L^p$

An inequality in $L^p$ spaces

$\lim_{p\rightarrow 0}\int_X|f|^p\,d\mu=\mu(\{x\in X\,|\,f(x)\ne 0\})$

Integral notation $\int_G d\mu(x) f(x)$

Does Improper Riemann integrability of type 2 mean lebesgues integrability?

Is the map $p\mapsto\int_X |f|^p d\mu$ differentiable when $\log|f|\notin L^1$?

$\int_{D} \frac{x-y}{1+x+y} d(x,y)$ for $D=\{(x,y)\in\Bbb R^{2}|0<x+y<1, 0<x-y<1\}$ using subsitution

Minimum of a function defined by an integral

Cross-sectional measures of a set of positive measure

Standard notation or name for the measure defined by an integral over a function

Is this measurability arguement correct?

If a set has positive measure, do its slices have positive measure?

Measure theory proof review: extended real valued maesurable functions with the same integral

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