  Remark.9 in Bose-Dasgupta-Rubin (2002) review states that when a non-negative
integer-valued infinitely divisible law has an atom at unity then its support
cannot have any gaps. Here one has two questions. (i) Why there are no gaps and
(ii) Can there be gaps if the condition is not satisfied. Our investigation
with these questions in mind centers on the implications of having and not
having atoms at zero and unity. We give two examples/ constructions, which show
that the remark needs modification and we modify it.
