Category-measure duality: convexity, midpoint convexity and Berz sublinearity
Category-measure duality: convexity, midpoint convexity and Berz sublinearity
Category-measure duality concerns applications of Baire-category methods that have measure-theoretic analogues. The set-theoretic axiom needed in connection with the Baire category theorem is the Axiom of Dependent Choice, DC rather than the Axiom of Choice, AC. Berz used the Hahn–Banach theorem over $${\mathbb {Q}}$$ to prove that the graph of …