List questions from lebesgue-integral

Published on 26 Oct 2018 - 16:25

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When is the improper integral well-defined in multiple dimensions?

Published on 26 Mar 2026 - 14:19

304

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Approximating Darboux integrals with continuous functions

Published on 25 Mar 2026 - 20:32

11

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Can this sequence of integrals take small values outside a compact set?

Published on 11 Mar 2026 - 7:32

33

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Notation Question Measure Theory

Published on 29 Oct 2018 - 0:03

718

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Is $\frac {\sin^2(x)}{x^2}$ Lebesgue integrable on $[0,\infty)$?

Published on 26 Mar 2026 - 17:32

53

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Is my counterexample correct?

Published on 29 Oct 2018 - 10:28

77

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Show that $lim\int_{-n}^n f=\int_{\mathbb{R}} f$

Published on 29 Oct 2018 - 19:07

198

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Function that is Differentiable Everywhere but not of Bounded Variation

Published on 30 Oct 2018 - 15:30

49

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Show that $i(f) = \int_a^b f \,d\lambda$ and $s(f) = \int_a^b f \,d\lambda$

Published on 30 Oct 2018 - 20:30

441

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Using Dominated Convergence Theorem to interchange Integral and Taylor Series of Sine

Published on 30 Oct 2018 - 23:13

85

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Square integrability of the mean of a random field

Published on 26 Mar 2026 - 13:02

2.6k

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Show that for a positive integrable function $f$ there is a simple function $\eta$ such that $0 \leq \eta \leq f$ and $\int |f-\eta|<\epsilon$

Published on 01 Nov 2018 - 1:35

308

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Questions about Lebesgue differentiation theorem

Published on 01 Nov 2018 - 13:28

98

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$t \in \mathbb{R}$ so that $f(t)=\int_{0}^{+\infty}e^{-tx}\frac{\sin x}{x}dx, t\in\mathbb{R}$ exists

Published on 26 Mar 2026 - 17:34

List Question

pqr theorem from Lieb-Loss

When is the improper integral well-defined in multiple dimensions?

Approximating Darboux integrals with continuous functions

Can this sequence of integrals take small values outside a compact set?

Notation Question Measure Theory

Is $\frac {\sin^2(x)}{x^2}$ Lebesgue integrable on $[0,\infty)$?

Is my counterexample correct?

Show that $lim\int_{-n}^n f=\int_{\mathbb{R}} f$

Function that is Differentiable Everywhere but not of Bounded Variation

Show that $i(f) = \int_a^b f \,d\lambda$ and $s(f) = \int_a^b f \,d\lambda$

Using Dominated Convergence Theorem to interchange Integral and Taylor Series of Sine

Square integrability of the mean of a random field

Show that for a positive integrable function $f$ there is a simple function $\eta$ such that $0 \leq \eta \leq f$ and $\int |f-\eta|<\epsilon$

Questions about Lebesgue differentiation theorem

$t \in \mathbb{R}$ so that $f(t)=\int_{0}^{+\infty}e^{-tx}\frac{\sin x}{x}dx, t\in\mathbb{R}$ exists

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