  We present a set of global invariants, called "mass integrals", which can be
defined for a large class of asymptotically hyperbolic Riemannian manifolds.
When the "boundary at infinity" has spherical topology one single invariant is
obtained, called the mass; we show positivity thereof. We apply the definition
to conformally compactifiable manifolds, and show that the mass is
completion-independent. We also prove the result, closely related to the
problem at hand, that conformal completions of conformally compactifiable
manifolds are unique.
