On the Range of a Regenerative SequenceP. W. Glynn Stochastic Processes and Their Applications, Vol. 20, 105113 (1985) For a given countable partition of the range of a regenerative sequence {X_{n}: n≥0}, let Rn be the number of distinct sets in the partition visited by X up to time n. We study convergence issues associated with the range sequence {R_{n}: n≥0}. As an application, we generalize a theorem of Chosid and Isaac to Harris recurrent Markov chains.
