Lukeš / Lukes / Malý Integral Representation Theory

Applications to Convexity, Banach Spaces and Potential Theory
1. Auflage 2009
ISBN: 978-3-11-020321-9
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 35, 732 Seiten, Gewicht: 10 g

Reihe: De Gruyter Studies in Mathematics

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

Zielgruppe

Students of Mathematics, Researchers; Academic Libraries.

Autoren/Hrsg.

Lukeš, Jaroslav

Lukes, Jaroslav

Malý, Jan

Netuka, Ivan

Spurný, Jirí

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

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

Über Autor(innen)

Jaroslav Lukeš, Jan Malý, Ivan Netuka and Jiri Spurný, Charles University, Prague, Czech Republic.