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Other Representation Theorems in Linear Spaces

  • Kôsaku Yosida
Part of the Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete book series (GL, volume 123)

Abstract

In this chapter, we shall prove three representation theorems in linear spaces. The first one, the Krein-Milman theorem says that a non-void convex compact subset K of a locally convex linear topological space is equal to the closure of the convex hull of the extremal points of K. The other two theorems concern the representations of a vector lattice as point functions and as set functions.

Keywords

Linear Space Extremal Point Maximal Ideal Vector Lattice Representation Theorem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • Kôsaku Yosida
    • 1
  1. 1.Gakushuin UniversityTokyoJapan

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