  Evidence is provided for a conjecture that, in the continuum limit, the mean
of the causal set action of a causal set sprinkled into a globally hyperbolic
Lorentzian spacetime, M, of finite volume equals the Einstein Hilbert action of
M plus the volume of the co-dimension 2 intersection of the future boundary
with the past boundary. We give the heuristic argument for this conjecture and
analyse some examples in 2 dimensions and one example in 4 dimensions.
