On a capacitability problem raised in connection with linear programming

Abstract

in the case that Jίκ is not empty. This quantity has a potential theoretic meaning. In fact, Fuglede Q2] considered it in case Φ^>0, g—1 and / = 1 and denoted it by capiC We shall call it Fuglede's capacity in §11. For any set A C F, we define in § 1 an inner quantity M{(A) and an outer quantity Me(A) from M(K) in the same way as the inner capacity cap*A and the outer capacity cap*̂ 4 were defined from cap K in [2] . Ohtsuka orally raised the question as to when M{(A) is equal to Me(A). We shall give an answer to this question in the present paper. Kishi Q3] examined this problem in the case that X= Y, Φ(x, y) = Φ(y, x) >0 for all x, ye X, Φ is lower semicontinuous and g=f=l. His main result