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

1. ## 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?