Any nonsingular action of the full symmetric group is isomorphic to an action with invariant measure

2018/11/14 by Nessonov, Nikolay
#28C10 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1811.05802

Abstract

Let \mathfrakS_∞ denote the set of all bijections of natural numbers. Consider the action of \mathfrakS_∞ on a measure space ( X,\mathfrakM,μ), where μ is \mathfrakS_∞-quasi-invariant measure. We prove that there exists \mathfrakS_∞-invariant measure equivalent to μ.

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