AN AXIOMATIZATION OF EXTENSIONAL PROBABILITY-MEASURES

Replacing the demand of countable additivity (sigma-additivity), impos ed on probability measures by the classical Kolmogorov axiomatic, by a stronger axiom, and considering only probability measures taking thei r values in the Canter subset of the unit interval of real numbers, we obtain such an axiomatic system that each probability measure satisfy ing these axioms is extensional in the sense that probability values a scribed to measurable unions and intersections of measurable sets are functions of probability values ascribed to particular sets in questio n. Moreover, each such probability measure can be set into a one-to-on e correspondence with a boolean-valued probability measure taking its values in the set of all subsets of an infinite countable space, e. g. , the space of all natural numbers.