Other Representation Theorems in Linear Spaces

  • Kôsaku Yosida
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 123)


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.


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

© Springer-Verlag Berlin Heidelberg 1971

Authors and Affiliations

  • Kôsaku Yosida
    • 1
  1. 1.Research Institute for Mathematical SciencesUniversity of KyotoKyotoJapan

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