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In this chapter we present some applications of the classical ergodic theorems and related techniques in different areas of mathematics, namely probability, number theory and combinatorics. Thereby, we discuss laws of large numbers, Borel’s theorem on normal numbers, and the theorems of Furstenberg-Sárközy and Roth about patterns in large sets of natural numbers.

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First Applications of Ergodic Theorems

  • 章节

  • 发表日期：

    2025年

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  • Tanja Eisner,
  • Bálint Farkas

摘要

In this chapter we present some applications of the classical ergodic theorems and related techniques in different areas of mathematics, namely probability, number theory and combinatorics. Thereby, we discuss laws of large numbers, Borel’s theorem on normal numbers, and the theorems of Furstenberg-Sárközy and Roth about patterns in large sets of natural numbers.