In this chapter we develop some of the prerequisites in functional analysis for later chapters of this book. We derive a few basic results from Choquet theory of function cones (section 1) and a related general minimum principle (section 2) whereas section 3 gives an up-to-date version of Choquet’s capacitability theorem. In section 4 we present Bernstein’s theorem concerning the identity of completely monotone functions and Laplace transforms of measures on ℝ+. Finally, we prove Stampacchias’s general projection theorem for Hilbert spaces which will be needed in chapter VIII.
KeywordsCompact Subset Convex Cone Compact Space Borel Subset Numerical Function
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