Let $\Omega = \Omega_1 \times \cdots \times \Omega_n (n > 1)$ be a product of n Brelot harmonic spaces each of which has a bounded potential, and let K be a compact subset of Ω. Then, K is an n-polar ...

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) ...