Integral Representation Theory : : Applications to Convexity, Banach Spaces and Potential Theory / / Jaroslav Lukeš, Jan Malý, Ivan Netuka, Jirí Spurný.

• Superior document: Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package
• VerfasserIn: Lukeš, Jaroslav,; Malý, Jan,; Netuka, Ivan,; Spurný, Jirí,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2009]; ©2010
• Year of Publication: 2009
• Language: English
• Series: De Gruyter Studies in Mathematics , 35
• Physical Description: 1 online resource (715 p.)
• Other title: 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 --; Backmatter
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783110203219; 9783110494938; 9783110238570; 9783110238471; 9783110637205; 9783110219517; 9783110219524; 9783110219463
• ISSN: 0179-0986
• DOI: 10.1515/9783110203219
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Jaroslav Lukeš, Jan Malý, Ivan Netuka, Jirí Spurný.

This 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 Applications