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Equidecomposition in cardinal algebras

Volume 253 / 2021

Forte Shinko Fundamenta Mathematicae 253 (2021), 197-204 MSC: Primary 08A65; Secondary 28A60. DOI: 10.4064/fm922-6-2020 Published online: 21 September 2020

Abstract

Let $\Gamma $ be a countable group. A classical theorem of Thorisson states that if $X$ is a standard Borel $\Gamma $-space and $\mu $ and $\nu $ are Borel probability measures on $X$ which agree on every $\Gamma $-invariant subset, then $\mu $ and $\nu $ are equidecomposable, i.e. there are Borel measures $(\mu _\gamma )_{\gamma \in \Gamma }$ on $X$ such that $\mu = \sum _\gamma \mu _\gamma $ and $\nu = \sum _\gamma \gamma \mu _\gamma $. We establish a generalization of this result to cardinal algebras.

Authors

  • Forte ShinkoDivision of Physics, Mathematics and Astronomy
    California Institute of Technology
    1200 E. California Blvd.
    Pasadena, CA 91125, U.S.A.
    e-mail

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