List questions from lebesgue-measure

Published on 12 Apr 2026 - 2:00

62

Views

Understanding an the last step in proving the Poincaré inequality for smooth functions on $\mathbb{R}^n$.

Published on 12 Apr 2026 - 18:49

74

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Null set if intersection with preimage under a linear map is countable

Published on 12 Apr 2026 - 1:27

243

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Half spaces are measurable

Published on 12 Apr 2026 - 9:25

64

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Weak, strong and uniform convergence of operator on $L^p(\mathbb{R}^d)$

Published on 14 Apr 2026 - 4:02

38

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Fatou's lemma and $\limsup \int_C |f_n|^p d\mu$

Published on 14 Apr 2026 - 18:01

30

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References a ideas behind weight functions

Published on 12 Apr 2026 - 3:52

74

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Equivalence of different properties

Published on 11 Apr 2026 - 8:29

54

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If $x$ is a density point of $E$ , then dist$(x,E)=0$ for dist$(x,E)=$inf$\{|x-e|:e\in E\}$

Published on 13 Apr 2026 - 18:06

58

Views

Calculating a lower bound of Lebesgue measure of some Borel set

Published on 25 Mar 2026 - 17:20

169

Views

If there is a zero measure set with positive measure pre-image, is there a level set with positive measure?

Published on 11 Apr 2026 - 20:20

169

Views

Property of Lebesgue Density Point

Published on 11 Apr 2026 - 8:21

101

Views

Continuity of functions involving Lebesgue measure in proof of ham sandwich theorem

Published on 13 Apr 2026 - 10:55

83

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Is this sufficient to conclude $L^{1}$ convergence?

Published on 13 Apr 2026 - 15:09

125

Views

Approximating a simple function by a step function almost everywhere

Published on 12 Apr 2026 - 11:49

List Question

Integrating with respect to Lebesgue measure

Understanding an the last step in proving the Poincaré inequality for smooth functions on $\mathbb{R}^n$.

Null set if intersection with preimage under a linear map is countable

Half spaces are measurable

Weak, strong and uniform convergence of operator on $L^p(\mathbb{R}^d)$

Fatou's lemma and $\limsup \int_C |f_n|^p d\mu$

References a ideas behind weight functions

Equivalence of different properties

If $x$ is a density point of $E$ , then dist$(x,E)=0$ for dist$(x,E)=$inf$\{|x-e|:e\in E\}$

Calculating a lower bound of Lebesgue measure of some Borel set

If there is a zero measure set with positive measure pre-image, is there a level set with positive measure?

Property of Lebesgue Density Point

Continuity of functions involving Lebesgue measure in proof of ham sandwich theorem

Is this sufficient to conclude $L^{1}$ convergence?

Approximating a simple function by a step function almost everywhere

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