Measure Theory: Transplantation theorems for inner premeasures

  • Heinz KönigEmail author


The main result is a new transplantation theorem for the inner * premeasures of the author, with a few related theorems. These results have basic implications for example for the construction of Radon measures. They received a certain inspiration from the treatment of Radon measures in the treatise of Fremlin on measure theory.


Inner premeasures and their maximal inner extensions Transplantation theorems Radon premeasures and Radon measures 


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  1. 1.
    V. I. Bogachev, Measure Theory Vol. I-II, Springer-Verlag 2007.Google Scholar
  2. 2.
    D. H. Fremlin, Measure Theory Vol. 1-4, Torres Fremlin 2004-2006 (in a reference with number the first digit indicates the volume).Google Scholar
  3. 3.
    H. König, Measure and Integration: An Advanced Course in Basic Procedures and Applications, Springer-Verlag 1997, reprint 2009.Google Scholar
  4. 4.
    H. König, What are signed contents and measures? Math. Nachr. 204(1999), 101-124.Google Scholar
  5. 5.
    H. König, Upper envelopes of inner premeasures, Ann. Inst. Fourier 50(2000), 401-422.Google Scholar
  6. 6.
    H. König, Projective limits via inner premeasures and the true Wiener measure, Mediterr. J. Math. 1(2004), 3-42.Google Scholar
  7. 7.
    H. König, Stochastic processes in terms of inner premeasures. Note Mat. 25(2005/06), 1-30.Google Scholar
  8. 8.
    H. König, Measure and Integral: New foundations after one hundred years, Functional Analysis and Evolution Equations (The Günter Lumer Volume), Birkhäuser 2007, pp. 405-422, Preprint No. 175 (with reformulations) under
  9. 9.
    H. König, Measure and Integration: Characterization of the new maximal contents and measures, Operator Theory: Advances and Applications 201, Birkhäuser 2009, pp. 293-302.Google Scholar
  10. 10.
    H. König, Measure and Integration: The basic extension theorems, Positivity, published online 12 August 2010.Google Scholar

Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Fakultät für Mathematik und InformatikUniversität des SaarlandesSaarbrückenGermany

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