Question

Confused with the notation used in proof of monotone class theorem and the logic behind the proof

score 144 · Answer 1 · 2020-10-22 13:55:29

144

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Confused with the notation used in proof of monotone class theorem and the logic behind the proof

Published on 22 Oct 2020 - 13:55

score 168 · Answer 2 · 2020-11-16 07:43:46

168

Views

Monotone convergence theorem for a decreasing recursive sequence from $n>n_0$

Published on 16 Nov 2020 - 7:43

score 53 · Answer 3 · 2020-11-18 22:52:08

53

Views

Show that ${ \mu(A \times B)=\mu_1(A) \cdot \mu_2(B) }$

Published on 18 Nov 2020 - 22:52

score 45 · Answer 4 · 2020-11-22 19:27:28

45

Views

No-monotone sequence

Published on 22 Nov 2020 - 19:27

score 108 · Answer 5 · 2020-12-05 17:54:20

108

Views

Compute inf and sup of a set A

Published on 05 Dec 2020 - 17:54

score 129 · Answer 6 · 2020-12-16 08:43:22

129

Views

Extending measure on Field to $\sigma$-Field

Published on 16 Dec 2020 - 8:43

score 119 · Answer 7 · 2021-01-19 14:35:26

119

Views

Using the monotone class argument to prove martingale property

Published on 19 Jan 2021 - 14:35

score 130 · Answer 8 · 2021-03-01 09:51:23

130

Views

Procedure to show martingale property

Published on 01 Mar 2021 - 9:51

score 39 · Answer 9 · 2021-12-02 14:53:42

39

Views

Absolute continuity of a measure in the intervals implies absolute continuity of borel measures?

Published on 02 Dec 2021 - 14:53

score 390 · Answer 10 · 2022-02-04 09:50:35

390

Views

Sigma algebra generated by bounded continuous functions on $\mathbb{R}$

Published on 04 Feb 2022 - 9:50

score 43 · Answer 11 · 2022-03-26 17:36:02

43

Views

monotone class theorem when $\Omega\not\in\mathcal A$, but $\Omega=\bigcup_{n\in\mathbb N}Ω_n$ for some $(Ω_n)_{n\in\mathbb N}\subseteq\mathcal A$

Published on 26 Mar 2022 - 17:36

score 40 · Answer 12 · 2022-04-22 03:23:24

40

Views

Find a family $\mathscr{F}$ such that $\mathscr{F}\subset \mathcal{M}\subset{\Phi_\mathscr{F}}$ with proper subsets.

Published on 22 Apr 2022 - 3:23

score 34 · Answer 13 · 2022-05-17 06:43:47

34

Views

$(X,\Sigma,\mu)$ be a probability space, $A\subset\Sigma$ be a field s.t. $\Sigma=\sigma(A)$.Prove inf$\{\mu(E\Delta F):F\in A\}=0\forall E\in\Sigma$

Published on 17 May 2022 - 6:43

score 74 · Answer 14 · 2022-09-23 00:22:58

74

Views

Let $G$ be an algebra. Then the smallest monotone class containing $G$ coincides with the smallest $\lambda$-system containing $G$

Published on 23 Sep 2022 - 0:22

score 199 · Answer 15 · 2022-09-23 10:25:05

199

Views

Dynkin's $\pi-\lambda$ theorem is equivalent to monotone class theorem

Published on 23 Sep 2022 - 10:25

List Question

Confused with the notation used in proof of monotone class theorem and the logic behind the proof

Monotone convergence theorem for a decreasing recursive sequence from $n>n_0$

Show that ${ \mu(A \times B)=\mu_1(A) \cdot \mu_2(B) }$

No-monotone sequence

Compute inf and sup of a set A

Extending measure on Field to $\sigma$-Field

Using the monotone class argument to prove martingale property

Procedure to show martingale property

Absolute continuity of a measure in the intervals implies absolute continuity of borel measures?

Sigma algebra generated by bounded continuous functions on $\mathbb{R}$

monotone class theorem when $\Omega\not\in\mathcal A$, but $\Omega=\bigcup_{n\in\mathbb N}Ω_n$ for some $(Ω_n)_{n\in\mathbb N}\subseteq\mathcal A$

Find a family $\mathscr{F}$ such that $\mathscr{F}\subset \mathcal{M}\subset{\Phi_\mathscr{F}}$ with proper subsets.

$(X,\Sigma,\mu)$ be a probability space, $A\subset\Sigma$ be a field s.t. $\Sigma=\sigma(A)$.Prove inf$\{\mu(E\Delta F):F\in A\}=0\forall E\in\Sigma$

Let $G$ be an algebra. Then the smallest monotone class containing $G$ coincides with the smallest $\lambda$-system containing $G$

Dynkin's $\pi-\lambda$ theorem is equivalent to monotone class theorem

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