A nonuniform version of the theorem of Radon-Nikodým in the finitely additive case with applications to extensions of finitely additive set functions
Proc. Amer. Math. Soc. 113 (1991), 651-654
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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.
P. S. Bhaskara Rao and M.
Bhaskara Rao, Theory of charges, Pure and Applied Mathematics,
vol. 109, Academic Press Inc. [Harcourt Brace Jovanovich Publishers],
New York, 1983. A study of finitely additive measures; With a foreword by
D. M. Stone. MR
N. Dunford and J. Schwartz, Linear operators, Part I, Interscience, New York, 1964.
- K. P. S. Bhaskara Rao and M. Bhaskara Rao, Theory of charges, Academic Press, New York, 1983. MR 751777 (86f:28006)
- N. Dunford and J. Schwartz, Linear operators, Part I, Interscience, New York, 1964.
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Nonuniform version of the Radon-Nikodym theorem,
finitely-additive set functions
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