Scholarlink

For an mpt of a probability space, the Poincaré Recurrence Theorem (Theorem 2.1 ) guarantees infinitely many returns to a positive-measure set, but makes no assertion about the frequency of returns. The Ergodic Theorems, discussed in this section, extract quantitative facts about frequencies and averages from the property of measure preservation. These are surprising and very deep results; they are also the most used in the subject.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Ergodic Theorems

  • 章节

  • 发表日期：

    2026年

查看全文
  • Alex Blumenthal,
  • Lai-Sang Young

摘要

For an mpt of a probability space, the Poincaré Recurrence Theorem (Theorem 2.1 ) guarantees infinitely many returns to a positive-measure set, but makes no assertion about the frequency of returns. The Ergodic Theorems, discussed in this section, extract quantitative facts about frequencies and averages from the property of measure preservation. These are surprising and very deep results; they are also the most used in the subject.