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A question about a sequence of sets with positive measure

score 71 · Answer 1 · 2019-01-08 08:12:36

71

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A question about a sequence of sets with positive measure

Published on 08 Jan 2019 - 8:12

score 1.1k · Answer 2 · 2019-01-08 16:43:40

1.1k

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If $m(E)=m_(E_1)+m_(E_2)$ , then $E_1$ and $E_2$ are measurable

Published on 08 Jan 2019 - 16:43

score 52 · Answer 3 · 2026-03-28 14:37:15

52

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For which parameters the integrals are convergent?

Published on 28 Mar 2026 - 14:37

score 425 · Answer 4 · 2026-03-25 10:56:57

425

Views

Is there a dense set in $\mathbb{R}$ with outer measure $1$? And what about with the Density Topology?

Published on 25 Mar 2026 - 10:56

score 36 · Answer 5 · 2019-01-09 16:38:05

36

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The image $f(A)$ of a measurable subset $A \subset \mathbb{R}$ is also measurable under $f(x) = ax + b$

Published on 09 Jan 2019 - 16:38

score 2.5k · Answer 6 · 2019-01-09 16:51:26

2.5k

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Show that Lebesgue measure is translation-invariant.

Published on 09 Jan 2019 - 16:51

score 78 · Answer 7 · 2026-03-28 14:37:52

78

Views

Calculate $\lim_{n \to \infty} \int_{\mathbb{R_{+}}} \exp((\cos^n x) -x) d\lambda(x)$

Published on 28 Mar 2026 - 14:37

score 507 · Answer 8 · 2026-03-25 06:05:04

507

Views

An application of Lebesgue Differentiation Theorem

Published on 25 Mar 2026 - 6:05

score 1.2k · Answer 9 · 2019-01-10 16:56:32

1.2k

Views

Help save this proof about the regularity of the lebesgue measure on $\mathbb{R}^d$

Published on 10 Jan 2019 - 16:56

score 506 · Answer 10 · 2026-03-25 06:05:14

506

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Motivation usage of Gramian Matrix for Integration on Submanifolds

Published on 25 Mar 2026 - 6:05

score 702 · Answer 11 · 2019-01-11 13:31:23

702

Views

$\mathrm{ess\, sup}(f)=\text{sup}(f)$ for a continuous non negative function $f$

Published on 11 Jan 2019 - 13:31

score 97 · Answer 12 · 2026-03-25 11:24:31

97

Views

What is the most elegant known proof of $m^(A) \leq \sum_{n} m^(A_n)$ when $A = \bigcup_n A_n$?

Published on 25 Mar 2026 - 11:24

score 116 · Answer 13 · 2026-03-28 18:01:51

116

Views

Monotone Convergence Theorem in calculating Lebesgue Integral

Published on 28 Mar 2026 - 18:01

score 173 · Answer 14 · 2019-01-12 17:16:04

173

Views

Example of a subset of $\mathbb{R}^2$ which is not $\sigma$-finite under Lebesgue measure?

Published on 12 Jan 2019 - 17:16

score 393 · Answer 15 · 2026-03-28 16:12:58

393

Views

Lebesgue Integral, an example

Published on 28 Mar 2026 - 16:12

List Question

A question about a sequence of sets with positive measure

If $m(E)=m_(E_1)+m_(E_2)$ , then $E_1$ and $E_2$ are measurable

For which parameters the integrals are convergent?

Is there a dense set in $\mathbb{R}$ with outer measure $1$? And what about with the Density Topology?

The image $f(A)$ of a measurable subset $A \subset \mathbb{R}$ is also measurable under $f(x) = ax + b$

Show that Lebesgue measure is translation-invariant.

Calculate $\lim_{n \to \infty} \int_{\mathbb{R_{+}}} \exp((\cos^n x) -x) d\lambda(x)$

An application of Lebesgue Differentiation Theorem

Help save this proof about the regularity of the lebesgue measure on $\mathbb{R}^d$

Motivation usage of Gramian Matrix for Integration on Submanifolds

$\mathrm{ess\, sup}(f)=\text{sup}(f)$ for a continuous non negative function $f$

What is the most elegant known proof of $m^(A) \leq \sum_{n} m^(A_n)$ when $A = \bigcup_n A_n$?

Monotone Convergence Theorem in calculating Lebesgue Integral

Example of a subset of $\mathbb{R}^2$ which is not $\sigma$-finite under Lebesgue measure?

Lebesgue Integral, an example

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