On Mixing-Like Notions in Infinite Measure

Measurable dynamical systems are defined on a measure space, such as the unit interval or the real line, with a transformation or map acting on the space. After discussing dynamical properties for probability spaces such as ergodicity, weak mixing, and mixing, we consider analogs of mixing and weak mixing in infinite measure, and present related examples and definitions that are the result of research with undergraduates. Rank-one transformations are introduced and used to construct the main examples.