04183nam 2200817Ia 450 991078070690332120200520144314.01-282-71436-897866127143683-11-020321-910.1515/9783110203219(CKB)2500000000002754(EBL)511787(OCoLC)651048124(SSID)ssj0000420661(PQKBManifestationID)11296193(PQKBTitleCode)TC0000420661(PQKBWorkID)10405790(PQKB)10703013(MiAaPQ)EBC511787(DE-B1597)33451(OCoLC)840443909(OCoLC)948655947(DE-B1597)9783110203219(Au-PeEL)EBL511787(CaPaEBR)ebr10373465(CaONFJC)MIL271436(PPN)175534527(EXLCZ)99250000000000275420091012d2010 uy 0engur|||||||||||txtccrIntegral representation theory[electronic resource] applications to convexity, banach spaces and potential theory /Jaroslav Lukeš ... [et al.]Berlin ;New York Walter de Gruyterc20101 online resource (731 p.)De Gruyter studies in mathematics ;35Description based upon print version of record.3-11-020320-0 Includes bibliographical references and index. Frontmatter -- Contents -- 1 Prologue -- 2 Compact convex sets -- 3 Choquet theory of function spaces -- 4 Affine functions on compact convex sets -- 5 Perfect classes of functions and representation of affine functions -- 6 Simplicial function spaces -- 7 Choquet theory of function cones -- 8 Choquet-like sets -- 9 Topologies on boundaries -- 10 Deeper results on function spaces and compact convex sets -- 11 Continuous and measurable selectors -- 12 Constructions of function spaces -- 13 Function spaces in potential theory and the Dirichlet problem -- 14 Applications -- BackmatterThis monograph presents the state of the art of convexity, with an emphasis to integral representation. The exposition is focused on Choquet's theory of function spaces with a link to compact convex sets. An important feature of the book is an interplay between various mathematical subjects, such as functional analysis, measure theory, descriptive set theory, Banach spaces theory and potential theory. A substantial part of the material is of fairly recent origin and many results appear in the book form for the first time. The text is self-contained and covers a wide range of applications. From the contents: Geometry of convex sets Choquet theory of function spaces Affine functions on compact convex sets Perfect classes of functions and representation of affine functions Simplicial function spaces Choquet's theory of function cones Topologies on boundaries Several results on function spaces and compact convex sets Continuous and measurable selectors Construction of function spaces Function spaces in potential theory and Dirichlet problem ApplicationsDe Gruyter studies in mathematics ;35.Functional analysisConvex domainsBanach spacesPotential theory (Mathematics)Integral representationsConvex Analysis.Dirichlet Problem.Functional Analysis.Partial Differential Equation.Potential Theory.Functional analysis.Convex domains.Banach spaces.Potential theory (Mathematics)Integral representations.515.7SK 600rvkLukeš Jaroslav, 59225Lukeš Jaroslav1940-59225MiAaPQMiAaPQMiAaPQBOOK9910780706903321Integral representation theory3832134UNINA