Abstract
This paper by A.N. Kolmogorov, together with those by Doob and Levy quoted below, laid the foundations of the theory of Markov processes dealing with homogeneous processes with a countable number of states. The peculiar effects taking place in these processes made them a separate branch of the general theory. At the same time, studies of the countable case helped to work out important concepts having a wider scope of application, such as the strong Markov property and boundary conditions for Markov processes.
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