For a group action, every group element acts on a set as a permutation. We consider a similar setting where each group element acts a permutation "modulo indeterminacy on finite subsets". We will indicate various natural occurrences of near actions. We will discuss realizability notions: is a given near action induced by a genuine action?
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Passcode: A group is called an ________ group if it admits an invariant mean. (8 letters, lowercase)