Given x 0 , a point of a convex subset C of a Euclidean space, the two following statements are proven to be equivalent: (i) every convex function f : C → ℝ is upper semi-continuous at x 0 , and (ii) ...

Let a statistical experiment be majorized in the sense that there is a non-negative measure such that each probability distribution has a density w.r.t. this measure. If the majorizing measure may be ...