Question

Can you implicitly construct a non-Borel subset $X \subset \mathbb{R}$ such that $\overline{X} = \mathbb{R}$?

score 69 · Answer 1 · 2021-01-16 00:56:42

69

Views

Can you implicitly construct a non-Borel subset $X \subset \mathbb{R}$ such that $\overline{X} = \mathbb{R}$?

Published on 16 Jan 2021 - 0:56

score 87 · Answer 2 · 2021-01-16 01:47:14

87

Views

Result on subspace Borel $\sigma$-algebra: Sorgenfrey plane provides counterexample?

Published on 16 Jan 2021 - 1:47

score 80 · Answer 3 · 2021-01-16 21:04:42

80

Views

Show the inclusion $\mathcal{B}(\mathbb R)^{I}\supseteq Q$

Published on 16 Jan 2021 - 21:04

score 55 · Answer 4 · 2026-03-29 17:36:25

55

Views

If $\tau$ and $\tau'$ define the same borel sets, then $\tau=\tau'$

Published on 29 Mar 2026 - 17:36

score 63 · Answer 5 · 2021-01-21 10:47:11

63

Views

A function that is measurable on $(\mathbb{R}^n, \mathcal{B}(\mathbb{R}^n))$

Published on 21 Jan 2021 - 10:47

score 52 · Answer 6 · 2026-03-26 04:34:28

52

Views

Can we claim that $A \cap B$ or $A \cup B$ is not in $\mathcal{B}(\mathbb{R}^n))$?

Published on 26 Mar 2026 - 4:34

score 45 · Answer 7 · 2021-01-23 21:26:30

45

Views

How to show that a set is a sigma algebra

Published on 23 Jan 2021 - 21:26

score 32 · Answer 8 · 2021-01-26 18:46:53

32

Views

Is $\mathcal B(\mathbb R) \times \mathcal B(\mathbb R)$ closed under finite intersection?

Published on 26 Jan 2021 - 18:46

score 118 · Answer 9 · 2026-03-29 19:33:04

118

Views

Finer Polish topology which turns countably many given Borel sets to clopen sets

Published on 29 Mar 2026 - 19:33

score 290 · Answer 10 · 2026-03-26 04:30:06

290

Views

Borel algebra always strictly smaller than its completion?

Published on 26 Mar 2026 - 4:30

score 39 · Answer 11 · 2021-01-31 18:54:16

39

Views

Confusing question on $\sigma$ algebra

Published on 31 Jan 2021 - 18:54

score 34 · Answer 12 · 2026-03-29 19:26:09

34

Views

Iteratively constructing Borel sets

Published on 29 Mar 2026 - 19:26

score 81 · Answer 13 · 2026-03-28 21:06:48

81

Views

$(X,A)$, $(Y,B)$, $(X \times Y, A \otimes B)$ measurable spaces. How to show $A=\{\emptyset, X\}$ or $B=\{\emptyset, Y\}$?

Published on 28 Mar 2026 - 21:06

score 266 · Answer 14 · 2026-03-29 19:32:58

266

Views

Effros Borel structure

Published on 29 Mar 2026 - 19:32

score 42 · Answer 15 · 2021-02-10 21:36:08

42

Views

Real Borel sets are complex Borel sets

Published on 10 Feb 2021 - 21:36

List Question

Can you implicitly construct a non-Borel subset $X \subset \mathbb{R}$ such that $\overline{X} = \mathbb{R}$?

Result on subspace Borel $\sigma$-algebra: Sorgenfrey plane provides counterexample?

Show the inclusion $\mathcal{B}(\mathbb R)^{I}\supseteq Q$

If $\tau$ and $\tau'$ define the same borel sets, then $\tau=\tau'$

A function that is measurable on $(\mathbb{R}^n, \mathcal{B}(\mathbb{R}^n))$

Can we claim that $A \cap B$ or $A \cup B$ is not in $\mathcal{B}(\mathbb{R}^n))$?

How to show that a set is a sigma algebra

Is $\mathcal B(\mathbb R) \times \mathcal B(\mathbb R)$ closed under finite intersection?

Finer Polish topology which turns countably many given Borel sets to clopen sets

Borel algebra always strictly smaller than its completion?

Confusing question on $\sigma$ algebra

Iteratively constructing Borel sets

$(X,A)$, $(Y,B)$, $(X \times Y, A \otimes B)$ measurable spaces. How to show $A=\{\emptyset, X\}$ or $B=\{\emptyset, Y\}$?

Effros Borel structure

Real Borel sets are complex Borel sets

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