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Measure Theory: Transplantation theorems for inner premeasures

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Measure and Integration

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Abstract

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.

Mathematics Subject Classification (1991). 28A12, 28C15.

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References

  1. V. I. Bogachev, Measure Theory Vol. I-II, Springer-Verlag 2007.

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  2. D. H. Fremlin, Measure Theory Vol. 1-4, Torres Fremlin 2004-2006 (in a reference with number the first digit indicates the volume).

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  3. H. König, Measure and Integration: An Advanced Course in Basic Procedures and Applications, Springer-Verlag 1997, reprint 2009.

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  4. H. König, What are signed contents and measures? Math. Nachr. 204(1999), 101-124.

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  5. H. König, Upper envelopes of inner premeasures, Ann. Inst. Fourier 50(2000), 401-422.

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  6. H. König, Projective limits via inner premeasures and the true Wiener measure, Mediterr. J. Math. 1(2004), 3-42.

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  7. H. König, Stochastic processes in terms of inner premeasures. Note Mat. 25(2005/06), 1-30.

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  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 http://www.math.uni-sb.de.

  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.

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  10. H. König, Measure and Integration: The basic extension theorems, Positivity, published online 12 August 2010.

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Author information

Authors and Affiliations

  1. Fakultät für Mathematik und Informatik, Universität des Saarlandes, 66041, Saarbrücken, Germany

    Heinz König

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  1. Heinz König
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Correspondence to Heinz König .

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König, H. (2012). Measure Theory: Transplantation theorems for inner premeasures. In: Measure and Integration. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0382-3_25

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