02825nam 22005655 450 99646652360331620200704034536.03-540-87565-410.1007/978-3-540-87565-9(CKB)1000000000546314(SSID)ssj0000319286(PQKBManifestationID)11277208(PQKBTitleCode)TC0000319286(PQKBWorkID)10336417(PQKB)10587013(DE-He213)978-3-540-87565-9(MiAaPQ)EBC3063886(PPN)132868407(EXLCZ)99100000000054631420100301d2009 u| 0engurnn|008mamaatxtccrOperator-Valued Measures and Integrals for Cone-Valued Functions[electronic resource] /by Walter Roth1st ed. 2009.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2009.1 online resource (X, 356 p.) Lecture Notes in Mathematics,0075-8434 ;1964Bibliographic Level Mode of Issuance: Monograph3-540-87564-6 Includes bibliographical references (p. 345-352) and index.Locally Convex Cones -- Measures and Integrals. The General Theory -- Measures on Locally Compact Spaces.Integration theory deals with extended real-valued, vector-valued, or operator-valued measures and functions. Different approaches are applied in each of these cases using different techniques. The order structure of the (extended) real number system is used for real-valued functions and measures, whereas suprema and infima are replaced with topological limits in the vector-valued case. A novel approach employing more general structures, locally convex cones, which are natural generalizations of locally convex vector spaces, is introduced here. This setting allows developing a general theory of integration which simultaneously deals with all of the above-mentioned cases.Lecture Notes in Mathematics,0075-8434 ;1964Measure theoryFunctional analysisMeasure and Integrationhttps://scigraph.springernature.com/ontologies/product-market-codes/M12120Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Measure theory.Functional analysis.Measure and Integration.Functional Analysis.515.42Roth Walterauthttp://id.loc.gov/vocabulary/relators/aut350426BOOK996466523603316Operator-valued measures and integrals for cone-valued functions230313UNISA