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This chapter is devoted to nilsystems and their remarkable algebraic and ergodic properties, such as everywhere convergence of multiple polynomial ergodic averages for continuous functions. As will be discussed in Chap. 15 , nilsystems serve as building blocks for general (regular) measure-preserving systems.

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Nilsystems

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  • 发表日期：

    2025年

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  • Tanja Eisner,
  • Bálint Farkas

摘要

This chapter is devoted to nilsystems and their remarkable algebraic and ergodic properties, such as everywhere convergence of multiple polynomial ergodic averages for continuous functions. As will be discussed in Chap. 15 , nilsystems serve as building blocks for general (regular) measure-preserving systems.