strong mixing

强混合

Dynamical Systems · Graduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: measure-theoretic mixing · mixing

Translation evidence: Literature usage

Meaning in context

A probability-preserving map is strongly mixing if μ(A∩T−nB)→μ(A)μ(B)\mu(A\cap T^{-n}B)\to\mu(A)\mu(B) for every fixed pair of measurable events A,BA,B.

保概率变换在时间间隔趋于无穷时，任意固定两事件的交概率趋于各自概率之积的性质。

Example

The fair binary Bernoulli shift is strongly mixing by eventual independence of separated cylinder blocks.

Usage and distinctions

This fixed-event definition differs from uniform mixing coefficients of stochastic processes and from topological mixing.

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Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Henk Bruin — Notes on Ergodic TheorySection 12, Mixing and weak mixing, Definition 13 · Checked 2026-10-14

Translation sources

  1. 何伟鲲 — 遍历论课程大纲（中国科学院大学）大纲内容，第二章 混合性，第1节 强混合、弱混合 · Checked 2026-10-14
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