Jones, Frank2016-04-222016-04-221972Bachman, Howard Floyd. "A characterization of the tail _-field for certain Markov chains." (1972) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/90089">https://hdl.handle.net/1911/90089</a>.https://hdl.handle.net/1911/90089If C(v,P) is a countable state, recurrent, aperiodic and irreducible Markov Chain with stationary probabilities, the measure of any set of the tail a-field is equal to either zero or one. Although recurrent Markov chains have trivial tail a-fields this is not in general true for transient chains. However the tail g-field for two merging independent Markov chains is trivial. Investigating the invariant measurable sets of 0 leads to the solution of a functional equation of the general form pf = f.36 ppengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.ThesisRICE1125reformatted digitalThesis Math. 1972 Bachmann