ABSTRACT
The following concept of a dentable1 subset of a Banach space X is essential for the study of the Radon-Nikodym Theorem and the Martingale Convergence Theorem in Banach spaces:
Definition 2.1.1. A set A ⊂ X is said to be dentable if, for every ǫ > 0, there exists an x ∈ A such that x /∈ conv(A \Bǫ(x)), where conv(A) denotes the closed convex hull of A, and Bǫ(x) stands for the ball in X with center at x, and radius ǫ.
