A nonuniform version of the theorem of Radon-Nikodým in the finitely additive case with applications to extensions of finitely additive set functions
Abstract: For it is shown that the existence of a net of nonnegative functions that are primitive relative to and satisfy , is equivalent to the condition , i.e. for some implies . Furthermore, as an application it is proved that for satisfying and any extension of , where denotes some algebra of subsets of containing , there exists some extension of such that is valid.
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Keywords: Nonuniform version of the Radon-Nikodym theorem, finitely-additive set functions
Article copyright: © Copyright 1991 American Mathematical Society