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  3. Convexity
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    • Publisher:
      Cambridge University Press
      Publication date:
      June 2011
      May 2011
      ISBN:
      9780511910135
      9781107007314
      DOI:
      https://doi.org/10.1017/CBO9780511910135
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.64kg, 356 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis
      Series:
      Cambridge Tracts in Mathematics (187)
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis
    Series:
    Cambridge Tracts in Mathematics (187)
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    Book description

    Convexity is important in theoretical aspects of mathematics and also for economists and physicists. In this monograph the author provides a comprehensive insight into convex sets and functions including the infinite-dimensional case and emphasizing the analytic point of view. Chapter one introduces the reader to the basic definitions and ideas that play central roles throughout the book. The rest of the book is divided into four parts: convexity and topology on infinite-dimensional spaces; Loewner's theorem; extreme points of convex sets and related issues, including the Krein–Milman theorem and Choquet theory; and a discussion of convexity and inequalities. The connections between disparate topics are clearly explained, giving the reader a thorough understanding of how convexity is useful as an analytic tool. A final chapter overviews the subject's history and explores further some of the themes mentioned earlier. This is an excellent resource for anyone interested in this central topic.

    Reviews

    "Simon's monograph is a valuable addition to the literature on convexity that will inspire many minds enchanted by the beauty and power of the cornerstone of functional analysis."
    S. Kutateladze, Mathematical Reviews

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