“Place functions”: alias continuous functions on the Stone space

Abstract:

Caratheodory’s system of place functions on a Boolean $\sigma$-ring is shown to be canonically isomorphic—order and algebraically—to the system of continuous extended real-valued functions over its Stone space. This enables one to dispense with the imperspicuous formulae and calculations of [CL] in favor of the more straightforward and familiar ones of function spaces; and to subsume the proposed generalization of integration under standard treatment.