03190nam 22005895 450 991014459900332120250724091932.03-540-48719-010.1007/b76887(CKB)1000000000233195(SSID)ssj0000324361(PQKBManifestationID)12087617(PQKBTitleCode)TC0000324361(PQKBWorkID)10313825(PQKB)10671252(DE-He213)978-3-540-48719-7(MiAaPQ)EBC3073233(PPN)155205757(EXLCZ)99100000000023319520121227d2001 u| 0engurnn#008mamaatxt$2 rdacontentcrdamediacrrdacarrierLectures on Choquet's Theorem /by Robert R. Phelps2nd ed. 2001.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2001.1 online resource (X, 130 p.)Lecture Notes in Mathematics,1617-9692 ;17573-540-41834-2 Includes bibliographical references and index.The Krein-Milman theorem as an integral representation theorem -- Application of the Krein-Milman theorem to completely monotonic functions -- Choquet’s theorem: The metrizable case. -- The Choquet-Bishop-de Leeuw existence theorem -- Applications to Rainwater’s and Haydon’s theorems -- A new setting: The Choquet boundary -- Applications of the Choquet boundary to resolvents -- The Choquet boundary for uniform algebras -- The Choquet boundary and approximation theory -- Uniqueness of representing measures. -- Properties of the resultant map -- Application to invariant and ergodic measures -- A method for extending the representation theorems: Caps -- A different method for extending the representation theorems -- Orderings and dilations of measures -- Additional Topics.A well written, readable and easily accessible introduction to "Choquet theory", which treats the representation of elements of a compact convex set as integral averages over extreme points of the set. The interest in this material arises both from its appealing geometrical nature as well as its extraordinarily wide range of application to areas ranging from approximation theory to ergodic theory. Many of these applications are treated in this book. This second edition is an expanded and updated version of what has become a classic basic reference in the subject.Lecture Notes in Mathematics,1617-9692 ;1757Potential theory (Mathematics)Functional analysisPotential TheoryFunctional AnalysisPotential theory (Mathematics)Functional analysis.Potential Theory.Functional Analysis.515/.73Phelps Robert Rauthttp://id.loc.gov/vocabulary/relators/aut60176MiAaPQMiAaPQMiAaPQBOOK9910144599003321Lectures on Choquet's theorem378122UNINA