G acts via isometries on a set X, and A,B are subsets of X. Prove that the relation A~B is an equivalence relation on subsets of X iff A and B are G-equidecomposable.(adsbygoogle = window.adsbygoogle || []).push({});

I think this has to do with the Banach-Schroder theorem, but am not sure. I know it is a definition in group theory, but am not sure how to prove it since it seem pretty self explanitory to me.

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# G-equidecomposable and equivalence relation

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