Integration theory of observables

N. S. Kronfli

pp. 497-502

in: Clifford A. Hooker (ed), The logico-algebraic approach to quantum mechanics I, Berlin, Springer, 1975

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 space X* of the Banach space of states X. Each bounded observable is furthermore represented by an element u* of X* such that for any proper state p ∈ X, u*(p) is the expectation value of u when the system is in the state p.