Total progeny of a branching process
= Total progeny of a branching process
{title2=$T=\sum_{j\geq0}Z_j$}
= Total progeny
{synonym}
The total progeny counts all individuals, including the initial ancestor, in a <Galton-Watson process>. It is infinite on survival. If the offspring mean is $m<1$, the <expected generation size in a Galton-Watson process> and the <monotone convergence theorem> give $\mathbb ET=1/(1-m)$.