On the Sobczyk-Hammer decomposition of additive set functions
Abstract: It is observed that continuity for charges is equivalent to the absence of two-valued minorants. This characterization forms the basis of a new short proof within a functional-analytic context of a decomposition theorem by A. Sobczyk and P. C. Hammer  for charges on a field into a continuous part and a part which can be written as a sum of at most two-valued charges on . A counterexample shows that in general the decomposition of a charge into a nonatomic part and a part which has no nonnull nonatomic minorant is not unique.
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Keywords: Continuous resp. nonatomic charges, Krein-Milman representation theorem, decomposition theorem
Article copyright: © Copyright 1982 American Mathematical Society