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We investigate the $x\log x$ condition for a general (Crump--Mode--Jagers)multi-type branching process with a general type space by constructing asize-biased population measure that relates to the ordinary population measurevia an intrinsic martingale $W_t$. Sufficiency of the $x\log x$ condition for anon-degenerate limit of $W_t$ is proved and conditions for necessity areinvestigated.

Size-biased branching population measures and the multi-type $x\log x$ condition