List questions from lebesgue-integral

Published on 26 Jul 2016 - 13:17

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Practicality of the Lebesgue integral

Published on 26 Jul 2016 - 23:51

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Do you need to understand measure theory to learn Lebesgue integration?

Published on 27 Jul 2016 - 8:02

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Bound on $p$-norm of power of function.

Published on 07 Apr 2026 - 4:45

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Let $f \in L^1(\mathbb{R}), F(x)=\int_{-\infty}^x f(y) \text{d}y, F \in L^1(\mathbb{R})$ then $F$ vanishes at infinity

Published on 28 Jul 2016 - 20:45

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Is the Lebesgue decomposition only meaningful for measures which are supported on different sets?

Published on 31 Jul 2016 - 21:42

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Is the $L^2$ limit of a sequence of symmetric functions also symmetric?

Published on 02 Aug 2016 - 5:03

331

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Is there any measure of "randomly defined" functions?

Published on 02 Aug 2016 - 14:37

367

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How to prove that a function is in fact $L_1$?

Published on 02 Aug 2016 - 14:40

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Log-convexity of the p-norms of a fixed function

Published on 07 Apr 2026 - 4:49

178

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How to show that $\chi_R(x) \nabla \frac 1{|x|} \in L^1(\mathbb R^3) \cap L^{3/2}(\mathbb R^3)$

Published on 05 Aug 2016 - 16:40

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$f$ Lebesgue integrable, showing $f$ is constant almost everywhere

Published on 05 Aug 2016 - 18:18

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Limit of a sequence of measurable function.

Published on 07 Aug 2016 - 3:58

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How to generalize the integral invariant property: $\int_{\mathbb R} e^{-r^2}dr = \int_{\mathbb R} e^{-(r+t)^2}dr $

Published on 08 Aug 2016 - 12:55

470

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How to show that $\mu$ is $\sigma$-finite

Published on 08 Aug 2016 - 15:53

List Question

Integrals w.r.t. measure $A\mapsto \int_Agd\mu$

Practicality of the Lebesgue integral

Do you need to understand measure theory to learn Lebesgue integration?

Bound on $p$-norm of power of function.

Let $f \in L^1(\mathbb{R}), F(x)=\int_{-\infty}^x f(y) \text{d}y, F \in L^1(\mathbb{R})$ then $F$ vanishes at infinity

Is the Lebesgue decomposition only meaningful for measures which are supported on different sets?

Is the $L^2$ limit of a sequence of symmetric functions also symmetric?

Is there any measure of "randomly defined" functions?

How to prove that a function is in fact $L_1$?

Log-convexity of the p-norms of a fixed function

How to show that $\chi_R(x) \nabla \frac 1{|x|} \in L^1(\mathbb R^3) \cap L^{3/2}(\mathbb R^3)$

$f$ Lebesgue integrable, showing $f$ is constant almost everywhere

Limit of a sequence of measurable function.

How to generalize the integral invariant property: $\int_{\mathbb R} e^{-r^2}dr = \int_{\mathbb R} e^{-(r+t)^2}dr $

How to show that $\mu$ is $\sigma$-finite

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