Abstract
Villegas' axiom of monotone continuity for comparative probabilities is shown to be sufficient for compatibility with submeasures C (Ortiz, 1980, th. 8), while the axiom of non-existence of atoms together with the above mentioned one characterize the subclass of atomless comparative probabilities that can be represented by probability measures. The properties of these submeasures C have driven us to propose a new axiom, that together with monotone continuity, are sufficient for compatibility of atomic and purely atomic comparative probabilities with probability measures. Finally we present methods for constructing such probability measures from submeasures C.
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