Doeblin's big limit theorem

Doeblin regarded his paper(²) as his hardest work. The big limit is that ofP(ⁿ)(x, E) asn tends to infinity, in a measurable non-topologized space. An exposition of part one of this paper was published in Ref. 1. This is the exposition of part two, which contains some reparation as well as clarification.Doeblin's great contributions to probability theory were remembered at a conference 50 Years after Doeblin: Developments in the Theory of Markov Chains, Markov Processes and Sums of Random Variables held at Blaubeuren. Germany November 2–7, 1991. Professor Chung contributed this article to further celebrate this occasion. The editor thanks him.