I do not have a thorough knowledge of measure-theoretic probability and Markov chain but I would start to learn by myself soon, but for few research-related works, I have to understand the theme of this paper. It would be a great help if someone explain me in a simple way what the paper has conveyed.
Invariant measures for Markov processes arising from iterated function systems with place-dependent probabilities M. F. BARNSLEY (), S. G. DEMKO, J. H. ELTON () and J. S. GERONIMO (**) School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332
A meta answer: this paper is both technical and fairly old, so if you are planning on using its results in your own research, you should keep in mind the possibility that there there have been improvements on the results in the past 30 years.
Several years ago I tried to see if I could use its results in a paper of mine. I found (1) that it was hard checking its hypotheses in my problem situation, and (2) it turned out its contractivity assumptions did not hold in my problem after all.
What you might want to do is read it in conjunction with Meyn and Tweedie's book on Markov chains, and translate the former into the latter's language as you go.