  There are two fundamental results in the classical theory of metric
Diophantine approximation: Khintchine's theorem and Jarnik's theorem. The
former relates the size of the set of well approximable numbers, expressed in
terms of Lebesgue measure, to the behavior of a certain volume sum. The latter
is a Hausdorff measure version of the former. We start by discussing these
theorems and show that they are both in fact a simple consequence of the notion
of `local ubiquity'. The local ubiquity framework introduced here is a much
simplified and more transparent version of that in \cite{memoirs}. Furthermore,
it leads to a single local ubiquity theorem that unifies the Lebesgue and
Hausdorff theories. As an application of our framework we consider the theory
of metric Diophantine approximation on limit sets of Kleinian groups. In
particular, we obtain a general Hausdorff measure version of Sullivan's
logarithm law for geodesics -- an aspect overlooked in \cite{memoirs}.
