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Stopping times definiton

  1. Jun 15, 2010 #1
    Hi this is more of a set theory question really, i'm a bit confused,

    say [tex] \mathcal{F} [/tex] is collections of sets, and [tex] \mathcal{F}_n [/tex] is a sequence of sub collections of sets and say [tex] B_{1}, B_{2} .... [/tex] is a sequence of sets
    what does the following mean [tex] \mathcal{S} = \{ A \in \mathcal{F} \colon A \cap B_{n} \in \mathcal{F}_n \forall n \in \mathbb{N} \} [/tex]

    for an element to be a member of the set [tex] \mathcal{S} [/tex] which of the conditons must be statisfy
    does this mean if [tex] A \cap B_{1} \in \mathcal{F}_1 , \space A \cap B_{2} \in \mathcal{F}_2 ...[/tex] then it belongs to the set or
    does it mean all these conditons must be met of it to be a members of the set [tex] A \cap B_{1} \in \mathcal{F}_1 , \space A \cap B_{1} \in \mathcal{F}_2 , \space A \cap B_{1} \in \mathcal{F}_3 ...... [/tex] for each [tex] B_{1}, B_{2} ....[/tex]
  2. jcsd
  3. Jun 15, 2010 #2


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    The first is the correct interpretation, if [itex]A \cap B_1\in\mathcal{F}_1[/itex] and [itex]A \cap B_2\in\mathcal{F}_2[/itex], etc., for all n = 1, 2,..., then A is in the collection.
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