Generic behavior of a measure-preserving transformation

Abstract

Del Junco-Lemańczyk [3] showed that a generic measure preserving transformation satisfies a certain orthogonality conditions. More precisely,

The spectral form of Koopman representations of the group of measurable functions with values in the circle

“…As Q S contains the constant functions C, it suffices to show that r l − c → 0 converges to 0 for some c ∈ C. 1) .…”

“…, m n come from {1, −1}. It is natural to enquire, especially in light of the arguments in [9] and the main theorem of [1] as reformulated in [9, Section 4], if the conclusion can be strengthened so that (4.1) holds with arbitrary coefficients from Z × . Theorem 2.2 implies that this is impossible.…”