  A causal set is a countably infinite poset in which every element is above
finitely many others; causal sets are exactly the posets that have a linear
extension with the order-type of the natural numbers -- we call such a linear
extension a {\em natural extension}. We study probability measures on the set
of natural extensions of a causal set, especially those measures having the
property of {\em order-invariance}: if we condition on the set of the bottom
$k$ elements of the natural extension, each possible ordering among these $k$
elements is equally likely. We give sufficient conditions for the existence and
uniqueness of an order-invariant measure on the set of natural extensions of a
causal set.
