Sherman, Glen Aldridge Minimal paradoxical decomposition for Mycielski’s square. (English) Zbl 0767.51010 Fundam. Math. 139, No. 3, 151-165 (1991). 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. Reviewer: A.Szybiak (Kitchener) 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 Keywords:infinite bipartite graph; \((m,n)\)-paradoxical (sub)set; free abelian group; spherical and hyperbolic isometries; equidistant line; hyperbolic plane; Mycielski’s square PDFBibTeX XMLCite \textit{G. A. Sherman}, Fundam. Math. 139, No. 3, 151--165 (1991; Zbl 0767.51010) Full Text: DOI EuDML