The justification of some (often implicit) limit arguments used in the development of structured population models is discussed via two examples. The first example shows how a pair of sink-source terms may transform into a side condition relating the appearance of individuals in the interior of the individual state space to the outflow of individuals at its boundary. The second example considers the usual equation for size-dependent population growth in which it is implicitly assumed that

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... te finitely-sized young are produced from infinitesimal contributions by all potential parents. The main mathematical tool for dealing with these examples is the Trotter-Kato theorem for one-parameter semigroups of bounded linear operators.