  We give a new Hausdorff content bound for limsup sets, which is related to
Falconer's sets of large intersection. Falconer's sets of large intersection
satisfy a content bound for all balls in a space. In comparison, our main
theorem only assumes a scale-invariant bound for the balls forming the limit
superior set in question.
  We give four applications of these ideas and our main theorem: a new proof
and generalization of the mass transference principle related to Diophantine
approximations, a related result on random limsup sets, a new proof of
Federer's characterization of sets of finite perimeter and a statement
concerning generic paths and the measure theoretic boundary. The new general
mass transference principle transfers a content bound of one collection of
balls, to the content bound of another collection of sets -- however, this
content bound must hold on all balls in the space. The benefit of our approach
is greatly simplified arguments as well as new tools to estimate Hausdorff
content.
  The new methods allow for us to dispense with many of the assumptions in
prior work. Specifically, our general Mass Transference Principle, and bounds
on random limsup sets, do not assume Ahlfors regularity. Further, they apply to
any complete metric space. This generality is made possible by the fact that
our general Hausdorff content estimate applies to limsup sets in any complete
metric space.
