manuscripta mathematica

, Volume 2, Issue 3, pp 285–299 | Cite as

Verallgemeinerung eines Satzes von F. Riesz

  • Edgar Berz


Let X be a compact Hausdorff space, C(X) the class of all continuous functions f: X→R, considered as an ordered vector space over R with respect to its canonical order; furthermore let F be an order complete ordered vector space over R. A linear operator A: C(X)→F is called bounded, if it transforms each bounded set of C(X) into a bounded set of F.

The purpose of this paper is to represent such a bounded linear operator A: C(X)→F as an integral Af=∫ dμ with respect to some content μ, defined on the algebraa(X) which is generated by the open sets U⊂X.

This representation is unique, if μ is required to be regular (p. 11).


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Copyright information

© Springer-Verlag 1970

Authors and Affiliations

  • Edgar Berz
    • 1
  1. 1.Mathematisches Institut der Universität63 Gießen

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