Ergodic Theory

J. J. P. Veerman ()
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J. J. P. Veerman: Portland State University

Chapter Chapter 9 in Numbers from all Angles, 2026, pp 171-190 from Springer

Abstract: 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.

Date: 2026
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DOI: 10.1007/978-3-032-10000-9_9

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