  This is the third in a series of papers dealing with the algebraic theory of
infinite classical lattices. This paper presents a theory of single
measurements on a lattice which we represent as comprising a finite
subvolume--the system of measurement--immersed in an infinite surround or
``heat bath'' which determines the system's state. We consider the class of all
stationary distributions on the set of microcanonical states of the infinite
lattice. The theory addresses the question, ``For a lattice initially in state
A, say, what is the probability that measurement of a certain quantity will
take a value in (a,b)?'' Discussion includes description of the source of
randomness in a measurement as well as characterization of the given states A.
