LACZKOVICH, M; (1991) INVARIANT SIGNED MEASURES AND THE CANCELLATION LAW. P AM MATH SOC , 111 (2) 421 - 431.
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Let X be a set, and let the group G act on X. We show that, for every A, B subset-of X, the following are quivalent: (i) A and B are G-equidecomposable; and (ii) upsilon(A) = upsilon-(B) for every G-invariant finitely additive signed measure upsilon. If the sets and the pieces of the decompositions are restricted to belong to a given G-invariant field A, then (i) if-and-only-if (ii) if and only if the cancellation law (n[A] = n[B] only-if [A] = [B]) holds in the space (X, G, A). We show that the cancellation law may fail even if the transformation group G is Abelian.
|Title:||INVARIANT SIGNED MEASURES AND THE CANCELLATION LAW|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics|
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