Supercritical Branching Processes with Countably Many Types and the Size of Random Cantor Sets

Publisher Summary This chapter discusses supercritical branching processes with finitely many types and the size of random cantor sets. Practically, always some compactness condition is imposed on the space of types or it is assumed that the process can be approximated in some sense by a process with finitely many types, or with a compact set of types. The rather mild second moment assumption is reasonable if one wants to apply Chebyshev. However, some assumption of supercriticality is necessary for the theorem as is well known from the behavior of single-type branching processes.