Duality gaps which may occur in semi-infinite programs are shown to be interpretable as a phenomenon of an improper representation of the constraint set, u^TP_i \geqq c_i, i \varepsilon I. Thus, any semi-infinite system of linear inequalities has a canonically closed equivalent (with interior...

Discussion that was omitted from page 210 of the authors' article "Duality in Semi-Infinite Programs and Some Works of Haar and Caratheódory," Management Science, Vol. 9, No. 2 (January 1963).

By constructing a new infinite dimensional space for which the extreme point--linear independence and opposite sign theorems of Charnes and Cooper continue to hold, and, building on a little-known work of Haar (herein presented), an extended dual theorem comparable in precision and...