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monotone class

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Definition 1 A collection $\mathcal M$ of subsets of $\Omega$ is a monotone class if it is closed under increasing and decreasing sequences of sets, i.e.

$A_1 \subseteq A_2 \subseteq A_3 ,...\in \mathcal M \Rightarrow \bigcup A_n \in \mathcal M$
$A_1 \supseteq A_2 \supseteq A_3 ,...\in \mathcal M \Rightarrow \bigcap A_n \in \mathcal M$

"monotone class" is owned by fernsanz.

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Keywords:

Monotone class theorem, sigma algebra

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Cross-references: sequences, decreasing, increasing, closed under, subsets, collection
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This is version 2 of monotone class, born on 2007-05-21, modified 2007-05-21.
Object id is 9426, canonical name is MonotoneClass.
Accessed 1236 times total.

Classification:

28A05 (Measure and integration :: Classical measure theory :: Classes of sets , measurable sets, Suslin sets, analytic sets)

Pending Errata and Addenda

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