A Radon-Nikodym derivative for positive linear functionals

E. de Amo; M. Díaz Carrillo

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An exact functional Radon-Nikodym theorem for Daniell integrals

E. de Amo, I. Chitescu, M. Díaz Carrillo (2001)

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Given two positive Daniell integrals I and J, with J absolutely continuous with respect to I, we find sufficient conditions in order to obtain an exact Radon-Nikodym derivative f of J with respect to I. The procedure of obtaining f is constructive.

Two generalizations of Komlós' theorem with lower closure-type applications.

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We establish that the inequality of Radon is a particular case of Jensen's inequality. Starting from several refinements and counterparts of Jensen's inequality by Dragomir and Ionescu, we obtain a counterpart of Radon's inequality. In this way, using a result of Simić we find another counterpart of Radon's inequality. We obtain several applications using Mortici's inequality to improve Hölder's inequality and Liapunov's inequality. To determine the best bounds for some inequalities,...

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Some remarks on Radon-Nikodym compact spaces

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The class of quasi Radon-Nikodým compact spaces is introduced. We prove that this class is closed under countable products and continuous images. It includes the Radon-Nikodým compact spaces. Adapting Alster's proof we show that every quasi Radon-Nikodým and Corson compact space is Eberlein. This generalizes earlier results by J. Orihuela, W. Schachermayer, M. Valdivia and C. Stegall. Further the class of almost totally disconnected spaces is defined and it is shown that every quasi...

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Bray, William O. (1986)

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The support theorem for the complex Radon transform of distributions.

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A new characterization of Eberlein compacta

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We give a sufficient and necessary condition for a Radon-Nikodým compact space to be Eberlein compact in terms of a separable fibre connecting weak-* and norm approximation.

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