unique ergodicity

唯一遍历性

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Other names / variants: uniquely ergodic

Translation evidence: Literature usage

Meaning in context

A continuous self-map of a nonempty compact metric space is uniquely ergodic when it has exactly one invariant Borel probability measure.

非空紧致度量空间上的连续自映射只有一个不变Borel概率测度的性质。

Example

An irrational circle rotation has normalized length as its unique invariant probability measure.

Usage and distinctions

Uniqueness is among all invariant probability measures; it is not merely ergodicity of a preselected measure.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Henk Bruin — Notes on Ergodic TheorySection 3, Ergodicity and unique ergodicity · 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，第一章，第5节 唯一遍历性，Weyl等分布定理 · Checked 2026-10-14
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