Invariant signed measures and the cancellation law

Author:
M. Laczkovich

Journal:
Proc. Amer. Math. Soc. **111** (1991), 421-431

MSC:
Primary 28D15; Secondary 20B99

MathSciNet review:
1036988

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Abstract: Let be a set, and let the group act on . We show that, for every , the following are equivalent: (i) and are -equidecomposable; and (ii) for every -invariant finitely additive signed measure . If the sets and the pieces of the decompositions are restricted to belong to a given -invariant field , then if and only if the cancellation law holds in the space . We show that the cancellation law may fail even if the transformation group is Abelian.

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DOI:
https://doi.org/10.1090/S0002-9939-1991-1036988-2

Article copyright:
© Copyright 1991
American Mathematical Society