Sur la propriété de branchement. (On the property of branching) (Q1079304)

Three lemmas (appearance; generation branching; time branching) given by \textit{P. Jagers} and \textit{O. Nerman} [Adv. Appl. Probab. 16, 221-259 (1984; Zbl 0535.60075)] for supercritical general branching processes are re-formulated by using a tree representation and the properties of a stopping line [see the preceding review, Zbl 0597.60078]. These lemmas are obvious consequences of the branching law and have a decisive part in the analysis of some fundamental, time- or generation-wise decomposition of the supercritical branching process into different family branches.