Nonsingular transformations that are ergodic with isometric coefficients and not weakly doubly ergodic (Q2088121)

The authors study weak double ergodicity and ergodicity with isometric coefficients for infinite measure-preserving ergodic dynamical systems. It is shown that there exist infinite measure-preserving transformations that are ergodic with isometric coefficients but are not weakly doubly ergodic, which confirms that these two notions are not equivalent in the case of infinite invariant measures. Under some technical assumptions it is proven that weak mixing with an infinite invariant measure implies ergodicity with isometric coefficients.