A well written, readable and easily accessible introduction to "Choquet theory", which treats the representation of elements of a compact convex set as integral averages over extreme points of the set. The interest in this material arises both from its appealing geometrical nature as well as its extraordinarily wide range of application to areas ranging from approximation theory to ergodic theory. Many of these applications are treated in this book. This second edition is an expanded and updated version of what has become a classic basic reference in the subject.
Lectures on Choquet's Theorem (Lecture Notes in Mathematics)
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First Sentence:
The simplest example of a theorem of the type with which we will be concerned is the following classical result of Minkowski (see the exercise on page 7). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
universal cap, maximal measure, nonnegative measure, locally convex space, compact convex subset, ergodic measures, representing measures, closed convex hull, compact base, closed convex cone, invariant probability measures, compact convex set, extreme points, affine functions Key Phrases - Capitalized Phrases (CAPs): (learn more)
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The simplest example of a theorem of the type with which we will be concerned is the following classical result of Minkowski (see the exercise on page 7). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
universal cap, maximal measure, nonnegative measure, locally convex space, compact convex subset, ergodic measures, representing measures, closed convex hull, compact base, closed convex cone, invariant probability measures, compact convex set, extreme points, affine functions Key Phrases - Capitalized Phrases (CAPs): (learn more)
Bishop-de Leeuw New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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- Forward-Backward Stochastic Differential Equations and their Applications (Lecture Notes in Mathematics) by Jin Ma in Back Matter (1), and Back Matter (2)
- Similarity Problems and Completely Bounded Maps (Lecture Notes in Mathematics) by Gilles Pisier in Back Matter (1), and Back Matter (2)
- Grothendieck Duality and Base Change (Lecture Notes in Mathematics) by Brian Conrad in Back Matter
- Total Colourings of Graphs (Lecture Notes in Mathematics (Springer-Verlag), 1623.) by H. P. Yap in Back Matter
- Sequences, Discrepancies and Applications (Lecture Notes in Mathematics) by Michael Drmota in Back Matter
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