Abstract
The main result is a new transplantation theorem for the inner \({\star}\) 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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V. I. Bogachev, Measure Theory Vol. I–II, Springer-Verlag 2007.
D. H. Fremlin, Measure Theory Vol. 1–4, Torres Fremlin 2004–2006 (in a reference with number the first digit indicates the volume).
H. König, Measure and Integration: An Advanced Course in Basic Procedures and Applications, Springer-Verlag 1997, reprint 2009.
König H.: What are signed contents and measures? Math. Nachr. 204, 101–124 (1999)
König H.: Upper envelopes of inner premeasures. Ann. Inst. Fourier 50, 401–422 (2000)
König H.: Projective limits via inner premeasures and the true Wiener measure. Mediterr. J. Math. 1, 3–42 (2004)
H. König, Stochastic processes in terms of inner premeasures. Note Mat. 25(2005/06), 1–30.
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.
H. König, Measure and Integration: Characterization of the new maximal contents and measures, Operator Theory: Advances and Applications 201, Birkhäuser 2009, pp. 293–302.
H. König, Measure and Integration: The basic extension theorems, Positivity, published online 12 August 2010.
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
König, H. Measure theory: transplantation theorems for inner premeasures. Arch. Math. 95, 493–500 (2010). https://doi.org/10.1007/s00013-010-0192-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-010-0192-3