List questions from lebesgue-measure

Published on 30 Oct 2018 - 1:04

178

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Euclidean Measure on Unit Sphere in $\Bbb{C}^n$

Published on 30 Oct 2018 - 11:57

584

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Lebesgue measure of the open unit cube

Published on 30 Oct 2018 - 12:00

96

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Why the Lemma below is true even if the measure $\mu$ is infinite?

Published on 22 Feb 2026 - 23:10

32

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Showing this sum is $\sim n^{3-\alpha}$.

Published on 31 Oct 2018 - 7:33

2.9k

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Under what circumstances is a characteristic function Riemann integrable?

Published on 26 Mar 2026 - 16:10

165

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Are all Jordan measurable sets Borel?

Published on 25 Mar 2026 - 6:00

672

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What is the Sigma Algebra generated by Jordan measurable sets?

Published on 25 Mar 2026 - 6:04

456

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Lebesgue Measurable Set which is not a union of a Borel set and a subset of a null $F_\sigma$ set?

Published on 25 Mar 2026 - 6:06

79

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Chi function with a set of finite measure

Published on 31 Oct 2018 - 22:18

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 27 Mar 2026 - 13:20

221

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If $f \in L^p$ with $1 \leq p < \infty$, then for any $\epsilon > 0$ there is a function $g$ with compact support such that $||f-g||_p < \epsilon$

Published on 01 Nov 2018 - 5:22

103

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If $z = f(x,y)$ is continuous on $\mathbb{R}^2$, then is $f(g_1(x), g_2(x))$ measurable, where $g_1$ and $g_2$ are measurable?

Published on 01 Nov 2018 - 16:37

98

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Why is it enough to consider simple functions on open intervals to prove the Riemann-Lebesgue lemma?

Published on 27 Mar 2026 - 14:59

37

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This property of of measurable sets and functions.

Published on 01 Nov 2018 - 22:20

List Question

Convergence in measure: two definitions

Euclidean Measure on Unit Sphere in $\Bbb{C}^n$

Lebesgue measure of the open unit cube

Why the Lemma below is true even if the measure $\mu$ is infinite?

Showing this sum is $\sim n^{3-\alpha}$.

Under what circumstances is a characteristic function Riemann integrable?

Are all Jordan measurable sets Borel?

What is the Sigma Algebra generated by Jordan measurable sets?

Lebesgue Measurable Set which is not a union of a Borel set and a subset of a null $F_\sigma$ set?

Chi function with a set of finite measure

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

If $f \in L^p$ with $1 \leq p < \infty$, then for any $\epsilon > 0$ there is a function $g$ with compact support such that $||f-g||_p < \epsilon$

If $z = f(x,y)$ is continuous on $\mathbb{R}^2$, then is $f(g_1(x), g_2(x))$ measurable, where $g_1$ and $g_2$ are measurable?

Why is it enough to consider simple functions on open intervals to prove the Riemann-Lebesgue lemma?

This property of of measurable sets and functions.

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