Question

Every separable complete metric space has a countable partition into nonempty Borel subsets

score 188 · Answer 1 · 2019-09-24 08:48:03

188

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Every separable complete metric space has a countable partition into nonempty Borel subsets

Published on 24 Sep 2019 - 8:48

score 53 · Answer 2 · 2026-03-25 17:22:21

53

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What does it mean to choose a sequence in a Borel fashion?

Published on 25 Mar 2026 - 17:22

score 1.3k · Answer 3 · 2014-09-27 20:11:56

1.3k

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Measurability of the floor function

Published on 27 Sep 2014 - 20:11

score 91 · Answer 4 · 2014-10-02 06:10:40

91

Views

Determine $\left \{ u\geq a \right \}$ for all $a\in \mathbb{R}$, and is $u$ $\mathcal B(\mathbb{R})/\mathcal B(\mathbb{R})$-measurable?

Published on 02 Oct 2014 - 6:10

score 29 · Answer 5 · 2019-10-02 17:18:25

29

Views

Are $\phi(X^2)$ and $\psi(Y^2)$ always independent where $\phi$ and $\psi$ are Borel-Measurable functions (X,Y are any two RVs)?

Published on 02 Oct 2019 - 17:18

score 84 · Answer 6 · 2019-10-06 06:05:18

84

Views

Universally Measurable and Continuous function

Published on 06 Oct 2019 - 6:05

score 57 · Answer 7 · 2026-03-24 01:49:51

57

Views

Show $\sum_{k=1}^\infty \frac{(1)^k}{k}1_{[k,k+1)}$ is Borel measurable

Published on 24 Mar 2026 - 1:49

score 38 · Answer 8 · 2019-10-13 13:36:26

38

Views

When is alternating series in $\mathcal{L}^p$

Published on 13 Oct 2019 - 13:36

score 149 · Answer 9 · 2019-10-13 22:45:10

149

Views

Which family of functions is the Lebesgue sigma algebra the initial sigma algebra of?

Published on 13 Oct 2019 - 22:45

score 11 · Answer 10 · 2026-03-21 12:48:05

11

Views

Regarding conditions required and specific topology to be induced on borel sets to define a specific measure

Published on 21 Mar 2026 - 12:48

score 174 · Answer 11 · 2019-10-14 19:29:11

174

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Any projection of a subset of $\mathbb{R}^2$ is Borel set

Published on 14 Oct 2019 - 19:29

score 1.1k · Answer 12 · 2019-10-15 01:19:07

1.1k

Views

$\pi$-system that generates the $\sigma$-algebra of Borel sets

Published on 15 Oct 2019 - 1:19

score 272 · Answer 13 · 2026-03-21 19:47:37

272

Views

Borel measure on the real line

Published on 21 Mar 2026 - 19:47

score 61 · Answer 14 · 2019-10-15 18:16:06

61

Views

Differential of a Lipschitz map is Borelian

Published on 15 Oct 2019 - 18:16

score 376 · Answer 15 · 2026-03-24 21:51:29

376

Views

Question on Borel Measurable Functions and Borel Sigma Algebras.

Published on 24 Mar 2026 - 21:51

List Question

Every separable complete metric space has a countable partition into nonempty Borel subsets

What does it mean to choose a sequence in a Borel fashion?

Measurability of the floor function

Determine $\left \{ u\geq a \right \}$ for all $a\in \mathbb{R}$, and is $u$ $\mathcal B(\mathbb{R})/\mathcal B(\mathbb{R})$-measurable?

Are $\phi(X^2)$ and $\psi(Y^2)$ always independent where $\phi$ and $\psi$ are Borel-Measurable functions (X,Y are any two RVs)?

Universally Measurable and Continuous function

Show $\sum_{k=1}^\infty \frac{(1)^k}{k}1_{[k,k+1)}$ is Borel measurable

When is alternating series in $\mathcal{L}^p$

Which family of functions is the Lebesgue sigma algebra the initial sigma algebra of?

Regarding conditions required and specific topology to be induced on borel sets to define a specific measure

Any projection of a subset of $\mathbb{R}^2$ is Borel set

$\pi$-system that generates the $\sigma$-algebra of Borel sets

Borel measure on the real line

Differential of a Lipschitz map is Borelian

Question on Borel Measurable Functions and Borel Sigma Algebras.

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