(a) during the interval (t, t + dt ), an individual existing at time t has (independently of its previous history) probability dt +o(dt )

(a) during the interval (t, t + dt ), an individual existing at time t has (independently of its previous history) probability λdt +o(dt ) of having a single offspring (twins, triplets, etc, being impossible) and a probability μdt + o(dt ) of dying, where λ and μ are absolute constants,