I encountered a trouble when I read theorem 3.17 in the book named "Brownian Motion, Martingales, and Stochastic Calculus". In this book, it first state that $X_{t+}:= \lim_{s \in D \atop s \downarrow \downarrow t}X_s(\omega)$ is well defined when the upcrossing number of $X_t(\omega)$ is finite. And then the author says that $X_{t+}$ is $\mathcal{F}_{t+}$-measurable with this definition.
I don't know how to prove it, can you help me to solve this question? Thanks in advance.