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I'm looking for a good resource that builds the theory of the Radon-Nikodym Property. I'm not particularly interested in the measure-theoretic characterisation; I'd like the geometry of Banach Spaces version, involving strongly exposed points of convex sets. If possible, I would also like the proofs to concentrate more a geometric approach over a convex/variational analysis approach, though this is not a deal-breaker. Thanks in advance.

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Chapter 5 of Geometric Nonlinear Functional Analysis by Benyamini and Lindenstrauss is the best geometrically-minded resource on RNP that I know.

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  • $\begingroup$ Thank you. I have one follow-up question. I'm reading through Theorem 5.11, at the bottom of page 106. I don't understand how Baire Category Theorem is being used. Do you know which BCT is being used, and how? $\endgroup$ – Theo Bendit Nov 19 '17 at 9:18
  • $\begingroup$ Never mind, I figured it out. $\endgroup$ – Theo Bendit Nov 19 '17 at 12:00

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