ergodic transformation

遍历变换

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Other names / variants: ergodicity · 遍历性

Translation evidence: Literature usage

Meaning in context

A probability-preserving map TT such that μ(T−1A△A)=0\mu(T^{-1}A\triangle A)=0 implies μ(A)=0\mu(A)=0 or 11 for every measurable AA.

保概率变换，其模零不变的任何可测事件只能具有概率0或1。

Example

An irrational circle rotation is ergodic for normalized length.

Usage and distinctions

Ergodicity depends on the chosen invariant measure and is weaker than weak mixing.

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Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Omri Sarig — Lecture Notes on Ergodic Theory§1.4, Definition 1.4 and Proposition 1.1 · Checked 2026-10-14

Translation sources

  1. 朱子阳 — 算术动力系统：代数数论专题 VI（作者主页讲义）§2 遍历论，定义2.1及段首“遍历变换” · Checked 2026-10-14
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