Return times and conjugates of an antiperiodic transformation

Abstract

Abstract Denote by G the group of all μ-preserving bijections of a Lebesgue probability space ( X , Σ, μ) and by C the conjugacy class of an antiperiodic transformation σ in G . We present several new results concerning the denseness of C in G with respect to various topologies. One of these asserts that given any weakly mixing transformation τ in G and any F with μ( F ) < 1, there is a transformation in C which agrees with τ a.e. on F .