Integral Representation Theory : Applications to Convexity, Banach Spaces and Potential Theory

Lukes, Jaroslav; Maly, Jan; Netuka, Ivan; Spurny, Jiri

ISBN 10: 3110203200 / ISBN 13: 9783110203202

Verlag: De Gruyter, 2010

Bestandsnummer des Verkäufers 8570085-n

Inhaltsangabe:

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

Über die Autorin bzw. den Autor:

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

Bibliografische Details

Titel: Integral Representation Theory : ...
Verlag: De Gruyter
Erscheinungsdatum: 2010
Einband: Hardcover
Zustand: New