Journal of Statistical Physics, Vol. 117, Nos. 1/2, October 2004. p. 281-300.
The problem of description of specifications by means of probability distributions in small volumes with infinite boundary conditions is considered. The description of specifications by means of n-specifications (consistent systems of probability distributions in volumes of cardinality bounded by n with infinite boundary conditions) is established under the condition of very weak positivity. Particular attention is paid to the most important case n = 1 which requires special considerations.