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Minimal paradoxical decomposition for Mycielski’s square. (English) Zbl 0767.51010

Main theorems: 1. There is no bounded 5-paradoxical (in the sense of Banach and Tarski) subset of the hyperbolic plane with positive Lebesgue measure: 2. Mycielski’s square in the hyperbolic plane admits a paradoxical decomposition with the partition number 6.

MSC:

51M10 Hyperbolic and elliptic geometries (general) and generalizations
28A99 Classical measure theory
03E05 Other combinatorial set theory
20F99 Special aspects of infinite or finite groups
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