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Math Help - Proof of ''The first date for which an event happens is a stopping time.''

  1. #1
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    Proof of ''The first date for which an event happens is a stopping time.''

    Suppose {X(t,\omega)} is a stochastic process on a filtered probability space (\Omega,\mathbb{F},P), and let A be any Borel set.

    Then, I want to show that the first date for which X(t,\omega)\in A is a stopping time.

    The attached pdf file is my proof. Is it complete?
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