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Ergodic Theory

In: Numbers from all Angles

Author

Listed:
  • J. J. P. Veerman

    (Portland State University)

Abstract

In this chapter, we venture seemingly very far from number theory. The reason is that we wish to investigate what properties “typical” real numbers have. By “typical” we mean “almost all”; and to define “almost all”, we have to delve fairly deeply into measure theory, one of the backbones of abstract analysis. In this chapter, we will point to the technical problems that need to be addressed, and then quickly state the most important result (the Birkhoff ergodic theorem). In Chap. 10 we will then move to the implications for number theory. The proof of the Birkhoff ergodic theorem will be postponed to Chap. 11.

Suggested Citation

  • J. J. P. Veerman, 2026. "Ergodic Theory," Springer Books, in: Numbers from all Angles, chapter 0, pages 171-190, Springer.
    • Handle: RePEc:spr:sprchp:978-3-032-10000-9_9
    DOI: 10.1007/978-3-032-10000-9_9
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