1. Reuter G. E. H. (1968) (Private communication).
2. This ensures that the fn (x), x ∈ (0, d] are well defined for n ≧ 0, and in conjunction with e.g., the continuity of f(x) at 0, implies fn (x) ↓ 0 for fixed x.
3. In both results, remarks analogous to the footnote 6 to Theorem B concerning the finite intervals, 0 ≦ x ≦ d, 0 < x ≦ d (closed on the right) apply.
4. Papangelou F. (1967) A lemma on the Galton-Watson process. Z. Wahrscheinlichkeitsth. (to appear).
5. A branching process with mean one and possibly infinite variance