Summary
In this paper generalizations of the classical Lebesgue-Radon-Nikodym type decomposition of additive set functions are obtained for pairs of vector measures when both measures take values in possibly different Banach spaces. Some applications of these results are made to (i) the representation of wearly compact operators on the spaces of integrable scalar functions relative to a vector measure to an arbitrary Banach space, and (ii) a problem of comparison of measures in inference theory. The abstract conditional expectations of operator valued strongly measurable and integrable random variables on a σ-finite space are briefly treated.
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Supported, in part, under the NSF Grants GP-1349 and GP-5921.
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Rao, M.M. Abstract Lebesgue-Radon-Nikodym theorems. Annali di Matematica 76, 107–131 (1967). https://doi.org/10.1007/BF02412231
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DOI: https://doi.org/10.1007/BF02412231