List questions from lebesgue-integral

Published on 17 May 2018 - 20:51

78

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How the function $f_n$ is a measurable function?

Published on 18 May 2018 - 1:47

100

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$\lim_{n\to\infty}\int f_n =0$ while $\limsup_{n\to\infty} f_n = +\infty$

Published on 18 May 2018 - 8:49

50

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Left/right hand (partial) derivative w.r.t $x$ of $\int_a^x f(x,t)dF(t)$, where $F$ is a CDF.

Published on 19 May 2018 - 3:13

111

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Integral using polar coordinates in high dimension.

Published on 19 May 2018 - 8:58

165

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Showing $\frac{e^{-ax} - e^{(a-1)x}}{1-e^{-x}}$ is integrable on $\mathbb{R}$

Published on 19 May 2018 - 16:33

71

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Can we exchange integral and limit?

Published on 20 May 2018 - 10:38

122

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Showing $\frac{1}{\sqrt{x(1-x)}}$ is integrable on $(0,1)$.

Published on 20 May 2018 - 13:50

73

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Stochastically dominating variables with same expectation

Published on 21 May 2018 - 0:44

114

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Jordan measure and indicator function discontinuities

Published on 21 May 2018 - 8:30

56

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The dual space of $L^1_0(\mathbb{R}^n)$, the subspace of $L^1 (\mathbb{R}^n)$ functions with vanishing integral.

Published on 25 Mar 2026 - 4:59

589

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$L^{p}_{loc}$ as a normed space

Published on 21 May 2018 - 11:27

181

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Derivative of $t \mapsto \int_\mathbb{R} (u+tv)^p$

Published on 21 May 2018 - 13:37

126

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Continuous functions defined on $[a, b]$ with values in a non-locally convex topological vector space that are not integrable?

Published on 23 May 2018 - 13:44

208

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Properties of Lebesgue integrable functions

Published on 25 May 2018 - 5:59

List Question

Fourier Transform, Schwarz Space Problem

How the function $f_n$ is a measurable function?

$\lim_{n\to\infty}\int f_n =0$ while $\limsup_{n\to\infty} f_n = +\infty$

Left/right hand (partial) derivative w.r.t $x$ of $\int_a^x f(x,t)dF(t)$, where $F$ is a CDF.

Integral using polar coordinates in high dimension.

Showing $\frac{e^{-ax} - e^{(a-1)x}}{1-e^{-x}}$ is integrable on $\mathbb{R}$

Can we exchange integral and limit?

Showing $\frac{1}{\sqrt{x(1-x)}}$ is integrable on $(0,1)$.

Stochastically dominating variables with same expectation

Jordan measure and indicator function discontinuities

The dual space of $L^1_0(\mathbb{R}^n)$, the subspace of $L^1 (\mathbb{R}^n)$ functions with vanishing integral.

$L^{p}_{loc}$ as a normed space

Derivative of $t \mapsto \int_\mathbb{R} (u+tv)^p$

Continuous functions defined on $[a, b]$ with values in a non-locally convex topological vector space that are not integrable?

Properties of Lebesgue integrable functions

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