On the use of purely finitely additive multipliers in mathematical programming

In this paper, duality results are obtained for the problem of finding α=inf{f(x):g(x)⩽0,g(x)∈Y,x∈C}, where the constrainst spaceY is someL∞-space, by using the norm topology ofY. The corresponding multiplier is the sum of a countably additive part and a purely finitely additive part. Conditions are given such that the purely finitely additive part may be discarded.