Generalized capacity and duality theorem in linear programming

Abstract

Recently certain results in the theory of games and linear programming have been applied to potential theory. We mention M. Nakai [2], B. Fuglede [1] and M. Ohtsuka [4]. Our paper is along this line. More precisely, the minimax theorem in the theory of games was applied to the theory of capacity in [4]. For a compact Hausdorff space K and an extended real-valued lower semicontinuous function Φ on K x K which is bounded below, the author established