source: John von Neumann studied the properties of the group of equivalences that make a paradoxical decomposition possible, identifying the class of amenable groups, for which no paradoxical decompositions exist.
target: John von Neumann studied the properties of a group of equivalences. This group made paradoxical decomposition possible. John identified a certain class of amenable groups. No paradoxical decompositions existed for this class.
references: John von Neumann studied the properties of a group of equivalences. This group made paradoxical decomposition possible. John identified a certain class of amenable groups. No paradoxical decompositions existed for this class.