THE X LOG X CONDITION FOR GENERAL BRANCHING-PROCESSES

The x log x condition is a fundamental criterion for the rate of growt h of a general branching process, being equivalent to non-degeneracy o f the limiting random variable. Tn this paper we adopt the ideas from Lyons, Pemantle and Peres (1995) to present a new proof of this well-k nown theorem. The idea is to compare the ordinary branching measure on the space of population trees with another measure, the size-biased m easure.