The summer after the New England Patriots won their first Super Bowl, I visited their training camp for a PBS NewsHour story on their — and the NFL’s — success, from the point of view of economics.

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) ...