An approximate functional Radon-Nikodym theorem |
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Authors: | E. De Amo I. Chitescu M. Díaz Carrillo |
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Affiliation: | (1) Depto. de Algebra y Análisis Matemático, Universidad de Almería, 04120 Almería, Spain;(2) Faculty of Mathematics, University of Bucharest, Str. Academiei 14, Bucharest, Romania;(3) Depto. de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain |
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Abstract: | We prove that for two linear and positive functionals (not necessarily Daniell)J andI on a lattice unitary algebraB of functions such thatJ is absolutely continuous with respect toI, one can expressJ as follows: , where (v m)m is a fixed sequence inB, for allf inB. This result is the “functional” similar of a previous deep result due to C. Fefferman. The comments and the counterexamples which we are introducing show that the main result (i.e sequential approximation) cannot be improved. |
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Keywords: | KeywordHeading" >A.M.S. Classification 28B05 26D15 |
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