The study of a locally convex space in terms of its dual is the central part of the modern theory of topological vector spaces, for it provides the setting for the deepest and most beautiful results of the subject; the present elaborate form of duality theory is largely due to Bourbaki  (cf. also Dieudonné  and Dieudonné-Schwartz ). The first five sections of this chapter contain the basic information, the remaining six being concerned with more refined and advanced results; as in the other chapters of the book, supplementary information can be found in the exercises. We proceed to survey the chapter briefly.
KeywordsNuclear Space Positive Radon Measure Continuous Linear Form Mackey Topology Strong Bidual
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