Question

Construct a measure space $(X,\mathcal{T},\mu)$ such that there is a $\{A_i\mid i \in I\}$ and a $r>0$ so that $\mu(A_i)<r$ but $\mu(\bigcup A_i)>r$.

score 29 · Answer 1 · 2022-09-06 00:06:00

29

Views

Construct a measure space $(X,\mathcal{T},\mu)$ such that there is a $\{A_i\mid i \in I\}$ and a $r>0$ so that $\mu(A_i)<r$ but $\mu(\bigcup A_i)>r$.

Published on 06 Sep 2022 - 0:06

score 58 · Answer 2 · 2026-03-25 20:10:59

58

Views

Order types of modified gap-embedding relations on finite trees

Published on 25 Mar 2026 - 20:10

score 83 · Answer 3 · 2022-09-17 12:45:35

83

Views

Is every infinite countable limit ordinal of form $\beta+ \omega$?

Published on 17 Sep 2022 - 12:45

score 91 · Answer 4 · 2022-10-01 20:29:01

91

Views

Help understanding countable and uncountable infinities

Published on 01 Oct 2022 - 20:29

score 49 · Answer 5 · 2022-10-03 10:51:02

49

Views

Prove that for all $\alpha \in \text{On}\setminus \{1\}$ there exists an arbitrarily large $\beta \in \text{On}$ such that :

Published on 03 Oct 2022 - 10:51

score 90 · Answer 6 · 2026-03-28 18:14:08

90

Views

Description of largest possible countable set / number

Published on 28 Mar 2026 - 18:14

score 45 · Answer 7 · 2022-10-12 16:39:45

45

Views

How to prove that the following object is not a set?

Published on 12 Oct 2022 - 16:39

score 121 · Answer 8 · 2022-10-14 23:43:14

121

Views

$\omega_1 +1$ is compact

Published on 14 Oct 2022 - 23:43

score 137 · Answer 9 · 2026-02-23 09:03:49

137

Views

$\omega_1$ is not Lindelof

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score 51 · Answer 10 · 2026-04-04 16:18:01

51

Views

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Published on 04 Apr 2026 - 16:18

score 31 · Answer 11 · 2026-03-28 12:14:03

31

Views

Dense Compact subset of $X = ((\beta(D) \times (\mathfrak{c}^+ + 1)) \setminus (\beta(D) \setminus D) \times \{\mathfrak{c}^+\})$

Published on 28 Mar 2026 - 12:14

score 53 · Answer 12 · 2022-10-21 14:10:57

53

Views

Ordinals of the $\varepsilon$ set

Published on 21 Oct 2022 - 14:10

score 114 · Answer 13 · 2022-10-22 16:20:35

114

Views

The set of limit ordinals in $\omega_1$ is unbounded

Published on 22 Oct 2022 - 16:20

score 98 · Answer 14 · 2026-03-25 21:49:47

98

Views

I don't understand this proof: Trichotomy for ordinals (by double transfinite induction)

Published on 25 Mar 2026 - 21:49

score 41 · Answer 15 · 2022-10-27 14:16:48

41

Views

Why is $2^\omega = \alpha^\omega$ defined as the limit of finite ordinals ( i.e. $ = \omega$)

Published on 27 Oct 2022 - 14:16

List Question

Construct a measure space $(X,\mathcal{T},\mu)$ such that there is a $\{A_i\mid i \in I\}$ and a $r>0$ so that $\mu(A_i)<r$ but $\mu(\bigcup A_i)>r$.

Order types of modified gap-embedding relations on finite trees

Is every infinite countable limit ordinal of form $\beta+ \omega$?

Help understanding countable and uncountable infinities

Prove that for all $\alpha \in \text{On}\setminus \{1\}$ there exists an arbitrarily large $\beta \in \text{On}$ such that :

Description of largest possible countable set / number

How to prove that the following object is not a set?

$\omega_1 +1$ is compact

$\omega_1$ is not Lindelof

"Hyper-pigeonhole principle": size of tail-avoiding sequence families

Dense Compact subset of $X = ((\beta(D) \times (\mathfrak{c}^+ + 1)) \setminus (\beta(D) \setminus D) \times \{\mathfrak{c}^+\})$

Ordinals of the $\varepsilon$ set

The set of limit ordinals in $\omega_1$ is unbounded

I don't understand this proof: Trichotomy for ordinals (by double transfinite induction)

Why is $2^\omega = \alpha^\omega$ defined as the limit of finite ordinals ( i.e. $ = \omega$)

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