On generalizations of Radon-Nikodym compact spaces

There are two notions weaker than that of Radon-Nikodym compact spaces and stronger than that of fragmentable compact spaces. They are the notions of "strongly fragmentable" compact spaces due to Reznichenko and that of "quasi-Radon-Nikodym" compact spaces due to Arvanitakis. We show below that the last two notions are equivalent. We also give an exposition of Arvanitakis's short topological proof of the fact that each quasi-Radon-Nikodym Corson compact space is Eberlein compact using the concept of "almost neighborhoods of the diagonal".