Right amenable left group sets and the Tarski-FØlner theorem

Abstract

‎We introduce right amenability‎, ‎right FØlner nets‎, ‎and right paradoxical decompositions for left homogeneous spaces and prove the Tarski-FØlner theorem for left homogeneous spaces with finite stabilisers‎. ‎It states that right amenability‎, ‎the existence of right FØlner nets‎, ‎and the non-existence of right paradoxical decompositions are equivalent‎.

Keywords

• ‎‎left group actions‎
• ‎right amenability‎
• ‎right FØlner nets‎
• ‎right paradoxical decompositions‎
• ‎Tarski-FØlner theorem