  This short note concerns the possible singular behaviour of moment generating
functions of finite measures at the boundary of their domain of existence. We
look closer at Example 7.3 in O. Barndorff-Nielsen's book "Information and
Exponential Families in Statistical Theory (1978)" and elaborate on the type of
exhibited singularity. Finally, another regularity problem is discussed and it
is solved through tensorizing two Barndorff- Nielsen's distributions.
