Integration theory of observables

Abstract

Representations of abstract observables on a generalised logic are given in terms of bounded vector-valued Borel measures on the real line whose ranges are in the dual spaceX ^* of the Banach space of statesX. Each bounded observable is furthermore represented by an elementu ^* ofX ^* such that for any proper statep ∈X, u ^* (p) is the expectation value ofu when the system is in the statep.