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A proof of the basic measure extension theorem of Carathéodory

  • Mathematik in Forschung, Lehre und Anwendung
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Abstract.

In this note a direct elementary proof of Carathéodory's measure extension theorem is presented. It is based on an approximation argument for outer measures where elements of the \(\sigma\)-algebra are approached by elements of the underlying algebra of sets with respect to the symmetric difference.

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  1. Heinrich-Heine-Universität Düsseldorf, Mathematisches Institut, Universitätsstr. 1, 40225 Düsseldorf. e-mail: janssena@uni-duesseldorf.de , , , , , , DE

    Arnold Janssen

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  1. Arnold Janssen
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Received: 3 April 2000 / Accepted: 20 September 2000

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Janssen, A. A proof of the basic measure extension theorem of Carathéodory. Math Semesterber 48, 103–106 (2001). https://doi.org/10.1007/PL00009932

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  • DOI: https://doi.org/10.1007/PL00009932

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