An algebraic theory of infinite classical lattices III: Theory of single measurements

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.