In June of 1940, shortly after the fall of Prance in which Doeblin died, I received a package of reprints sent from France by Fréchet. It was probably among those reprints that I first saw Doeblin's paper [1] cited. I was then a student at Kunming, China and had read Fréchet's book [2]. Kolmogorov's paper [3] which laid the foundation of the theory of Markov chains with denumerable states was not accessible to me, although the journal containing it might have been under the caves of Yunnanfu to escape Japanese bombing, as I reminisced at the Paul Lévy memorial in 19871. I read it later after learning Russian, and translated it in an exercise book which I still have. Kolmogorov mentioned Doeblin's independent work but did not state the two problems treated in [1]. I think Feller first showed that paper to me. Later Mrs. Doeblin sent me several of her son's reprints, among which was this one, with a cover but without the year of publication nor the number of the volume, testifying to the wartime conditions in France. What I remembered distinctly is that I asked a visitor, M.L., to report its content to a small audience, including Doob and Snell. Afterwards we had a good chuckle over it because the oral presentation did not sound any different from the rather obscure original script. The following year I was living in New York City and giving a course on limit theorems for sums of independent random variables at the Department of Mathematical Statistics of Columbia University, and the Korean war broke out. I must have tired of those sums and been looking for something else to think about. It was in this way that I returned to the first problem in [1]…