Show that, in the notation of Lemma 23.6 , (mathscr{A}_{sigma wedge tau}=mathscr{A}_{sigma} cap mathscr{A}_{tau}) for any two

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Show that, in the notation of Lemma 23.6 , \(\mathscr{A}_{\sigma \wedge \tau}=\mathscr{A}_{\sigma} \cap \mathscr{A}_{\tau}\) for any two stopping times \(\sigma, \tau\).

Data from lemma 23.6

Lemma 23.6 Let (X, A, An,) be a o-finite filtered measure space and , T stopping times. (1) O AT, O VT, o+k,

Proof (1) follows immediately from the identities {o^T

i.e. AEAT, hence Ao CAT. (iii) We have for all BEB(R) and ne No U {x} n} = = {uo  B} n {o

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