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- W1903172032 endingPage "670" @default.
- W1903172032 startingPage "599" @default.
- W1903172032 abstract "This chapter discusses the study of convex sets in infinite dimensional spaces that lies at the heart of the geometry of Banach spaces. For instance, the unit ball completely determines the metric properties of a Banach space, while its weak-compact convex dual unit ball plays a ubiquitous role. Fixed-point theorems are fundamental to many parts of analysis. An application of Choquet's theorem to ergodic measures (where the extreme points need not form a closed set) is also discussed in this chapter. In most applications of Choquet's theorem, the representing measure is unique. A closed face of a compact simplex is again a simplex. Every compact metric convex set can be represented as a section of a compact metric simplex with an affine subspace. The intersection of a directed (downward) family of compact simplices is a simplex." @default.
- W1903172032 created "2016-06-24" @default.
- W1903172032 creator A5023088510 @default.
- W1903172032 creator A5028382952 @default.
- W1903172032 creator A5080589332 @default.
- W1903172032 date "2001-01-01" @default.
- W1903172032 modified "2023-09-26" @default.
- W1903172032 title "Infinite Dimensional Convexity" @default.
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