List questions from lebesgue-integral

Published on 31 Mar 2014 - 11:57

50

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If $u \in L^2(\Omega)$, then $\text{sign}u \in L^2(\Omega)$?

Published on 31 Mar 2014 - 12:47

975

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Lebesgue integration: Existence of double integral, but not Lebesgue integrable.

Published on 31 Mar 2014 - 18:28

104

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Proving this is Lebesgue integrable using radial functions

Published on 01 Apr 2014 - 7:20

603

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Lebesgue integrability and measurable functions

Published on 01 Apr 2014 - 21:10

24

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condition for which we have an integrable function

Published on 02 Apr 2014 - 13:17

290

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Sobolev inequality in negative index

Published on 31 Mar 2026 - 7:05

114

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Weak absolute continuity of measures

Published on 02 Apr 2014 - 15:10

190

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Biorthogonal functions in $L^p$

Published on 02 Apr 2014 - 19:08

1.5k

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$f$ being a Lebesgue integrable function on $(0, a)$ implies that $g(x) = \int_x^a (f(t)/t)dt$ is also integrable.

Published on 03 Apr 2014 - 0:38

56

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For which a and b is $\int_0^{1/2} r^{a+n-1}|\log(r)|^b dr<\infty$?

Published on 03 Apr 2014 - 1:53

2.1k

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Lebesgue integral of a non-negative function.

Published on 03 Apr 2014 - 12:48

727

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Why is the topology of convergence in measure equivalent to this metric here?

Published on 03 Apr 2014 - 22:20

54

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lebesgue integral of $f(x^n)$

Published on 04 Apr 2014 - 12:23

765

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Integration of standard multivariate normal distribution

Published on 04 Apr 2014 - 12:48

List Question

Lebesgue Integration: Double Integral (Fubini)

If $u \in L^2(\Omega)$, then $\text{sign}u \in L^2(\Omega)$?

Lebesgue integration: Existence of double integral, but not Lebesgue integrable.

Proving this is Lebesgue integrable using radial functions

Lebesgue integrability and measurable functions

condition for which we have an integrable function

Sobolev inequality in negative index

Weak absolute continuity of measures

Biorthogonal functions in $L^p$

$f$ being a Lebesgue integrable function on $(0, a)$ implies that $g(x) = \int_x^a (f(t)/t)dt$ is also integrable.

For which a and b is $\int_0^{1/2} r^{a+n-1}|\log(r)|^b dr<\infty$?

Lebesgue integral of a non-negative function.

Why is the topology of convergence in measure equivalent to this metric here?

lebesgue integral of $f(x^n)$

Integration of standard multivariate normal distribution

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