ENGLISH

Integral representation theory: Applications to convexity, Banach spaces and potential theory

By Jaroslav Lukeš

Book information

Publisher
de Gruyter
Year
2010
ISBN
9783110203202, 3110203200
LCC
QA320 .I573 2010
Open Library ID
OL25211437M
Language
english
Format
PDF
Filesize
3 MB (2939150 bytes)
Series
De Gruyter Studies in Mathematics
Pages
732\732
Library
Kolxo3
Time added
2010-07-29 05:14:56

Description

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

Similar books