  In mathematical biology and the theory of electric networks the firing map of
an integrate-and-fire system is a notion of importance. In order to prove
useful properties of this map authors of previous papers assumed that the
stimulus function f of the system \dot{x}= f(t,x) is continuous and usually
periodic in the time variable. In this work we show that the required
properties of the firing map for the simplified model \dot{x}=f(t) still hold
if f \in L_{loc}^1(R) and f is an almost periodic function. Moreover, in this
way we prepare a formal framework for next study of a discrete dynamics of the
firing map arising from almost periodic stimulus that gives information on
consecutive resets (spikes).
