Given an event $A \subset \Omega$, a Markov chain $(X_n)$ on $\Omega$ and stopping time $T$ what is the formal definition of: "The event $A$ is determinated by $X_0, \ldots, X_T$". I have found this in the proof of Markov property and Strong Markov property on Markov chains book of James Norris and I don't understand the formal meaning.
Formal definition of: "The event $A$ is determinated by $X_0, \ldots, X_T$"
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markov-chains
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1$$A\in\sigma(X_0,\ldots,X_n)$$ – 2017-01-22
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0@Did Ok, I have modified the question – 2017-01-22
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2$$A=\bigcup_n(T=n)\cap A_n\qquad A_n\in\sigma(X_0,\ldots,X_n)$$ – 2017-01-22