On the set of values of a nonatomic, finitely additive, finite measure
On the set of values of a nonatomic, finitely additive, finite measure
A countably additive, nonatomic, finite measure takes on every value from zero to its maximum, inclusive, where, as throughout this note, it is to be understood that measures are non-negative.1The purpose of this note is to exhibit a counter-example, expressed as a theorem, which shows that finitely additive measures are …