Integral Representation Theory
Applications to Convexity, Banach Spaces and Potential Theory
1st Edition
Published on 22. December 2009
XVI, 715 pages
978-3-11-020321-9 (ISBN)
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
Reviews / Votes
"Incorporating many original results of the authors, the book is addressed both to students who can find a clear and thorough presentation of the basics of the integral theory, as well as for the advanced readers who find a substantial amount of recent results, appearing for the first time in book form."S. Cobzas in: Studia Universitatis Babes-Bolyai LV/2010More details
Other editions
Additional editions
Jaroslav Lukes | Jan Malý | Ivan Netuka
Integral Representation Theory
Applications to Convexity, Banach Spaces and Potential Theory
Book
01/2010
1st Edition
De Gruyter
€210.00
Shipment within 7-9 days
Jaroslav Lukes | Jan Malý | Ivan Netuka
Integral Representation Theory
Applications to Convexity, Banach Spaces and Potential Theory
Book
01/2010
1st Edition
De Gruyter
€209.00
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Persons
Jaroslav Lukes, Jan Malý, Ivan Netuka and Jiri Spurný, Charles University, Prague, Czech Republic.
Content
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
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
