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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.