I am reading Norris's "Markov Chains" and would appreciate an explanation of the following bit.
After stating the Markov property, it is said that (on page 4)
In general, any event A determined by $X_0, ...,X_m$ may be written as a countable disjoint union of elementary events $A=\bigcup_{k=1}^{\infty} A_k$
What are these $A_k$'s and why are there infinitely many of them? How does this follow from the Markov property?
Thanks.