Some remarks on Radon–Nikodym compact spaces
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 Radon–Nikodým space which is almost totally disconnected is actually a Radon–Nikodým compact space embeddable in the space of probability measures on a scattered compact space.