Gardner conjectured that if two bounded measurable sets A, B subset of Double-struck capital R-n are equidecomposable by a set of isometries Gamma generating an amenable group then A and B admit a measurable equidecomposition by all isometries. Ciesla and Sabok asked if there is a measurable equidecomposition using isometries only in the group generated by Gamma. We answer this question negatively
We construct for every $d \geq 2$ a $d$-regular acyclic measurably bipartite graphing that admits no...
Acknowledgement The authors wish to thank the referee for a very careful and precise reading of seve...
Abstract. Using the work of Cornulier-Valette and Whyte, we show that neither the Haagerup property ...
We give a sketch of proof that any two (Lebesgue) measurable subsets of the unit sphere in Rn, for n...
In 1924 Banach and Tarski demonstrated the existence of a paradoxical decomposition of the 3-ball B,...
Abstract. In 1924 Banach and Tarski demonstrated the existence of a paradoxical decomposition of the...
Laczkovich proved that if bounded subsets $A$ and $B$ of $R^k$ have the same non-zero Lebesgue measu...
We prove that every Schreier graph of a free Borel action of a finitely generated non-amenable group...
Laczkovich proved that if bounded subsets A and B of ❘k have the same non-zero Lebesgue measure and ...
Published: Inventiones Mathematicae, 177 (2009), 533-540International audienceWe give a positive ans...
We characterize hyperfinite bipartite graphings that admit measurable perfect matchings. In particul...
Abstract. We show that every locally finite bipartite Borel graph satisfy-ing a strengthening of Hal...
AbstractHarary, Robinson and Wormald (1978) proved that for a complete tripartite graph G = K (m, n,...
Joint work wih Claude Laflamme, Norbert Sauer and Robert Woodrow. Two structures are said to be $\e...
Joint work wih Claude Laflamme, Norbert Sauer and Robert Woodrow. Two structures are said to be $\e...
We construct for every $d \geq 2$ a $d$-regular acyclic measurably bipartite graphing that admits no...
Acknowledgement The authors wish to thank the referee for a very careful and precise reading of seve...
Abstract. Using the work of Cornulier-Valette and Whyte, we show that neither the Haagerup property ...
We give a sketch of proof that any two (Lebesgue) measurable subsets of the unit sphere in Rn, for n...
In 1924 Banach and Tarski demonstrated the existence of a paradoxical decomposition of the 3-ball B,...
Abstract. In 1924 Banach and Tarski demonstrated the existence of a paradoxical decomposition of the...
Laczkovich proved that if bounded subsets $A$ and $B$ of $R^k$ have the same non-zero Lebesgue measu...
We prove that every Schreier graph of a free Borel action of a finitely generated non-amenable group...
Laczkovich proved that if bounded subsets A and B of ❘k have the same non-zero Lebesgue measure and ...
Published: Inventiones Mathematicae, 177 (2009), 533-540International audienceWe give a positive ans...
We characterize hyperfinite bipartite graphings that admit measurable perfect matchings. In particul...
Abstract. We show that every locally finite bipartite Borel graph satisfy-ing a strengthening of Hal...
AbstractHarary, Robinson and Wormald (1978) proved that for a complete tripartite graph G = K (m, n,...
Joint work wih Claude Laflamme, Norbert Sauer and Robert Woodrow. Two structures are said to be $\e...
Joint work wih Claude Laflamme, Norbert Sauer and Robert Woodrow. Two structures are said to be $\e...
We construct for every $d \geq 2$ a $d$-regular acyclic measurably bipartite graphing that admits no...
Acknowledgement The authors wish to thank the referee for a very careful and precise reading of seve...
Abstract. Using the work of Cornulier-Valette and Whyte, we show that neither the Haagerup property ...
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