Extremal and monogenic additive set functions

Abstract

The extreme points of the convex set of all additive set functions on a field, which coincide on a subfield are characterized by a simple approximation property. It is proved that a stronger approximation property is characteristic for a so-called monogenic additive set function on a field, which can be generated uniquely by an additive set function on a subfield. Finally it is shown that a simple decomposition property must hold if the convex set above has a finite number of extreme points.