Integral Representation Theory

Applications to Convexity, Banach Spaces and Potential Theory

von Jaroslav Lukeš, Jan Malý, Ivan Netuka, Jirí Spurný

715 Seiten, Hardcover

Kurzbeschreibung des Verlags

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

• Reihe: De Gruyter Studies in Mathematics
• Themen: Mathematik und Naturwissenschaften Mathematik Mathematische Analysis, allgemein Funktionalanalysis und Abwandlungen
• ISBN: 9783110203202
• Sprache: Englisch
• Erscheinungsdatum: 14.01.2010
• Größe: 24 x 17 cm
• Verlag: De Gruyter