CHAPTER VIII Mixing

@inproceedings{Schmidt1995CHAPTERVM,
  title={CHAPTER VIII Mixing},
  author={Klaus Schmidt},
  year={1995}
}
Let d ≥ 1, and let T be a measure preserving Zd-action on a probability space (\(\mathop{Y},\,\mathfrak{J},\,{\mu}\)). A non-empty subset \(F\,\,{\subset} \mathop{{Z}^{d}}\) is mixing for T if, for all collections of sets \(\left\{{B}_{n}\,:\,{n}\,{\in}\,{F}\right\}\,{\subset}\,\mathfrak{J}\), \(lim \underline {{k{\rightarrow}\infty}}\,{\mu} \left({{\bigcap} {\underline{n{\in} F}}}\,{T}_{kn}(B_n) \right)\,= \prod \underline{n{\in}F}\mu (B_n)\) and non-mixing otherwise.