Group

Definition 1 A group is a non-empty set \(\Group\) together with a binary operation on \(\Group\), denoted "\(\GroupOperation{}{}\)", that combines any two elements \(\GroupElement\) and \(\GroupElement'\) of \(\Group\) to form an element of \(\Group\), denoted \(\GroupOperation{\GroupElement}{\GroupElement'}\), such that the following three requirements, known as group axioms, are satisfied:

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• Amenable
• Functional Analysis
• Measure Theory and Ergodic Theory
• Density
• Følner sequence
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• Kronecker Factor
• Furstenberg’s Correspondence Principle
• Erdős Cubes
• Factor Maps
• Recurrence and Ergodic Theorems
• A Short Proof of a Generalised Conjecture of Erdős for Amenable Groups
• Progressive Measures
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