  Property A was introduced by Yu as a non-equivariant analogue of amenability.
Nigel Higson posed the question of whether there is a homological
characterisation of property A. In this paper we answer Higson's question
affirmatively by constructing analogues of group cohomology and bounded
cohomology for a metric space X, and show that property A is equivalent to
vanishing cohomology. Using these cohomology theories we also give a
characterisation of property A in terms of the existence of an asymptotically
invariant mean on the space.
