Invertible measure-preserving transformations form a dense Gδ subset of all measure-preserving transformations on standard non-atomic probability spaces under the strong operator topology.
Halmos, Lectures on Ergodic Theory, Chelsea Publishing Company
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A generic transformation is invertible
Invertible measure-preserving transformations form a dense Gδ subset of all measure-preserving transformations on standard non-atomic probability spaces under the strong operator topology.