Key Takeaway: Limit theorems for Markov processes are derived from the set function P(x,A) and the set function P(x,A) for a fixed A and I.

Abstract

1. Notation. Let (X,X) be a measurable space. Let P(x,A) be transition probabilities: 1.1. P(x,A) is definedfor xeX and Ace and O_P(x,A)<1. 1.2. For a fixed x the set function P(x, ) is a measure on S. 1.3. For a fixed A E I the function P( *, A) is measurable. By measure we shall mean a countably additive, positive, finite measure. When we deal with finitely additive bounded measures we shall write p e ba(X, 1). On occasions we shall deal with a-finite, countably additive positive measures.