Softcover ISBN:  9781470443597 
Product Code:  CBMS/126 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
eBook ISBN:  9781470447175 
Product Code:  CBMS/126.E 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
Softcover ISBN:  9781470443597 
eBook: ISBN:  9781470447175 
Product Code:  CBMS/126.B 
List Price:  $110.00 $82.50 
MAA Member Price:  $99.00 $74.25 
AMS Member Price:  $88.00 $66.00 
Softcover ISBN:  9781470443597 
Product Code:  CBMS/126 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
eBook ISBN:  9781470447175 
Product Code:  CBMS/126.E 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
Softcover ISBN:  9781470443597 
eBook ISBN:  9781470447175 
Product Code:  CBMS/126.B 
List Price:  $110.00 $82.50 
MAA Member Price:  $99.00 $74.25 
AMS Member Price:  $88.00 $66.00 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 126; 2018; 83 ppMSC: Primary 52
Theory of valuations on convex sets is a classical part of convex geometry which goes back at least to the positive solution of the third Hilbert problem by M. Dehn in 1900. Since then the theory has undergone a multifaceted development. The author discusses some of Hadwiger's results on valuations on convex compact sets that are continuous in the Hausdorff metric. The book also discusses the KlainSchneider theorem as well as the proof of McMullen's conjecture, which led subsequently to many further applications and advances in the theory. The last section gives an overview of more recent developments in the theory of translationinvariant continuous valuations, some of which turn out to be useful in integral geometry.
This book grew out of lectures that were given in August 2015 at Kent State University in the framework of the NSF CBMS conference “Introduction to the Theory of Valuations on Convex Sets”. Only a basic background in general convexity is assumed.
ReadershipGraduate students and researchers interested in the theory of valuations on convex sets.

Table of Contents

Chapters

Introduction

Basic definitions and examples

McMullen’s decomposition theorem

Valuations on the line

McMullen’s description of $(n1)$homogeneous valuations

The KlainSchneider characterization of simple valuations

Digression on the theory of generalized functions on manifolds

The GoodeyWeil imbedding

Digression on vector bundles

The irreducibility theorem

Further developments


Additional Material

Reviews

For the newcomer to the field, the book gives a first orientation, insights into the underlying structures, and valuable hints to the original literature.
Rolf Schneider, Zentralblatt MATH 
This little book gives a very nice overview of a subject nearly at the cutting edge of research.
P. McMullen, Mathematical Reviews


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Theory of valuations on convex sets is a classical part of convex geometry which goes back at least to the positive solution of the third Hilbert problem by M. Dehn in 1900. Since then the theory has undergone a multifaceted development. The author discusses some of Hadwiger's results on valuations on convex compact sets that are continuous in the Hausdorff metric. The book also discusses the KlainSchneider theorem as well as the proof of McMullen's conjecture, which led subsequently to many further applications and advances in the theory. The last section gives an overview of more recent developments in the theory of translationinvariant continuous valuations, some of which turn out to be useful in integral geometry.
This book grew out of lectures that were given in August 2015 at Kent State University in the framework of the NSF CBMS conference “Introduction to the Theory of Valuations on Convex Sets”. Only a basic background in general convexity is assumed.
Graduate students and researchers interested in the theory of valuations on convex sets.

Chapters

Introduction

Basic definitions and examples

McMullen’s decomposition theorem

Valuations on the line

McMullen’s description of $(n1)$homogeneous valuations

The KlainSchneider characterization of simple valuations

Digression on the theory of generalized functions on manifolds

The GoodeyWeil imbedding

Digression on vector bundles

The irreducibility theorem

Further developments

For the newcomer to the field, the book gives a first orientation, insights into the underlying structures, and valuable hints to the original literature.
Rolf Schneider, Zentralblatt MATH 
This little book gives a very nice overview of a subject nearly at the cutting edge of research.
P. McMullen, Mathematical Reviews