Measure and Integration: Characterization of the new maximal contents and measures

  • Heinz KönigEmail author


The work of the author in measure and integration is based on parallel extension theories from inner and outer premeasures to their maximal extensions, both times in three different columns (finite, sequential, nonsequential). The present paper characterizes those contents and measures which occur as these maximal extensions.


Inner and outer premeasures and their maximal extensions complete saturated and SC contents and measures tame inner and outer premeasures quasi-Radon measures 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C. Berg, J.P.R. Christensen and P. Ressel, Harmonic Analysis on Semigroups. Springer 1984.Google Scholar
  2. 2.
    D.H. Fremlin, Topological Riesz Spaces and Measure Theory. Cambridge Univ. Press 1974.CrossRefGoogle Scholar
  3. 3.
    D.H. Fremlin, Measure Theory Vol. 1–4. Torres Fremlin 2000–2003 (in a numbered reference the first digit indicates its volume).".
  4. 4.
    H. König, Measure and Integration: An Advanced Course in Basic Procedures and Applications. Springer 1997.Google Scholar
  5. 5.
    H. König, Measure and Integration: Mutual generation of outer and inner premeasures. Annales Univ. Saraviensis Ser. Math. 9(1998) No. 2, 99–122.Google Scholar
  6. 6.
    H. König, Measure and Integration: An attempt at unified systematization. Rend. Istit. Mat. Univ. Trieste 34(2002), 155–214. Preprint No. 42 under
  7. 7.
    H. König, Measure and Integral: New foundations after one hundred years. In: Functional Analysis and Evolution Equations (The Günter Lumer Volume). Birkhäuser 2007, pp. 405–422. Preprint No. 175 under
  8. 8.
    J. Łoś and E. Marczewski, Extensions of measure. Fund.Math. 36(1949), 267–276.MathSciNetCrossRefGoogle Scholar
  9. 9.
    L. Schwartz, Radon Measures on Arbitrary Topological Spaces and Cylindrical Measures. Oxford Univ. Press 1973.zbMATHGoogle Scholar
  10. 10.
    F. Topsøe, Compactness in spaces of measures. Studia Math. 36(1970), 195–212.MathSciNetCrossRefGoogle Scholar
  11. 11.
    F. Topsøe, Topology and Measure. Lect. Notes Math. 133, Springer 1970.Google Scholar

Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Fakultät für Mathematik und InformatikUniversität des SaarlandesSaarbrückenGermany

Personalised recommendations