Question

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

score 147 · Answer 1 · 2026-03-31 13:29:40

147

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

Published on 31 Mar 2026 - 13:29

score 171 · Answer 2 · 2026-03-31 04:34:17

171

Views

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

Published on 31 Mar 2026 - 4:34

score 56 · Answer 3 · 2026-03-31 13:18:13

56

Views

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

Published on 31 Mar 2026 - 13:18

score 48 · Answer 4 · 2026-03-30 19:56:23

48

Views

No-monotone sequence

Published on 30 Mar 2026 - 19:56

score 111 · Answer 5 · 2026-03-30 19:17:10

111

Views

Compute inf and sup of a set A

Published on 30 Mar 2026 - 19:17

score 132 · Answer 6 · 2026-03-31 02:08:47

132

Views

Extending measure on Field to $\sigma$-Field

Published on 31 Mar 2026 - 2:08

score 122 · Answer 7 · 2026-03-31 07:16:42

122

Views

Using the monotone class argument to prove martingale property

Published on 31 Mar 2026 - 7:16

score 133 · Answer 8 · 2026-03-31 09:39:20

133

Views

Procedure to show martingale property

Published on 31 Mar 2026 - 9:39

score 42 · Answer 9 · 2026-03-31 06:49:56

42

Views

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

Published on 31 Mar 2026 - 6:49

score 393 · Answer 10 · 2026-03-31 02:53:58

393

Views

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

Published on 31 Mar 2026 - 2:53

score 46 · Answer 11 · 2026-03-30 19:55:36

46

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 30 Mar 2026 - 19:55

score 43 · Answer 12 · 2026-03-31 08:28:19

43

Views

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

Published on 31 Mar 2026 - 8:28

score 37 · Answer 13 · 2026-03-30 18:55:24

37

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 30 Mar 2026 - 18:55

score 77 · Answer 14 · 2026-03-31 14:49:09

77

Views

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

Published on 31 Mar 2026 - 14:49

score 201 · Answer 15 · 2026-03-29 22:39:42

201

Views

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

Published on 29 Mar 2026 - 22:39

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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