Multiplicative population processes

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Abstract
The theory of multiplicative (or branching) population processes where the states of each individual in the population range over a fixed finite set has been studied by a number of authors: see for example, Everett and Ulam, Kolmogorov and Sevastyanov, Harris; the continuous parameter case is treated in Arley; further references will be found in the books by Bartlett and Bharucha-Reid. The purpose of the present paper is to study the theory of such processes in the case where the individual state space is arbitrary (i.e., an abstract space).

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