Polish topologies on groups of non-singular transformations [article]

François Le Maître
2022 arXiv   pre-print
In this paper, we prove several results concerning Polish group topologies on groups of non-singular transformation. We first prove that the group of measure-preserving transformations of the real line whose support has finite measure carries no Polish group topology. We then characterize the Borel σ-finite measures λ on a standard Borel space for which the group of λ-preserving transformations has the automatic continuity property. We finally show that the natural Polish topology on the group
more » ... f all non-singular transformations is actually its only Polish group topology.
arXiv:2110.07289v2 fatcat:r3nevgwijjcircve5qhrxs7cga