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Introduction to the Theory of Valuations
 
Semyon Alesker Tel Aviv University, Tel Aviv, Israel
A co-publication of the AMS and CBMS
Introduction to the Theory of Valuations
Softcover ISBN:  978-1-4704-4359-7
Product Code:  CBMS/126
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $44.00
eBook ISBN:  978-1-4704-4717-5
Product Code:  CBMS/126.E
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $44.00
Softcover ISBN:  978-1-4704-4359-7
eBook: ISBN:  978-1-4704-4717-5
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
Introduction to the Theory of Valuations
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Introduction to the Theory of Valuations
Semyon Alesker Tel Aviv University, Tel Aviv, Israel
A co-publication of the AMS and CBMS
Softcover ISBN:  978-1-4704-4359-7
Product Code:  CBMS/126
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $44.00
eBook ISBN:  978-1-4704-4717-5
Product Code:  CBMS/126.E
List Price: $55.00
MAA Member Price: $49.50
AMS Member Price: $44.00
Softcover ISBN:  978-1-4704-4359-7
eBook ISBN:  978-1-4704-4717-5
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 Details
     
     
    CBMS Regional Conference Series in Mathematics
    Volume: 1262018; 83 pp
    MSC: 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 Klain-Schneider 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 translation-invariant 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.

    Readership

    Graduate 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 $(n-1)$-homogeneous valuations
    • The Klain-Schneider characterization of simple valuations
    • Digression on the theory of generalized functions on manifolds
    • The Goodey-Weil imbedding
    • Digression on vector bundles
    • The irreducibility theorem
    • Further developments
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 1262018; 83 pp
MSC: 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 Klain-Schneider 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 translation-invariant 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.

Readership

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 $(n-1)$-homogeneous valuations
  • The Klain-Schneider characterization of simple valuations
  • Digression on the theory of generalized functions on manifolds
  • The Goodey-Weil 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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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