Comments on (5), (14), (22), (30), and (31)

  • Burgess Davis
  • Renming Song
Part of the Selected Works in Probability and Statistics book series (SWPS)


During the two decades after the publication of the pioneering papers “Proof of the ergodic theorem” and “Proof the quasi-ergodic hypothesis” by Birkhoff [4] and von Neumann [18], but before the publication of “A general ergodic theorem” by Calderón in 1953, there were new proofs and generalizations of the results of Birkhoff and von Neumann given by many mathematicians. These include, among others, Khintchine, Hopf, Kolmogorov, F. Riesz, Yoshida, Kakutani, Wiener, Dunford, Pitt, Doob, and Zygmund. Much of this substantial body of work is referenced in [11], [15], and [16]. Explorations in many new directions have continued since then and have greatly expanded the connections and applications of ergodic theory to other parts of mathematics and beyond. Calderón’s 1953 paper (5) played an important role in this development.


Ergodic Theory Ergodic Theorem Ergodic Average Pointwise Ergodic Theorem Ergodic Group 
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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Mathematics and Department of StatisticsPurdue UniversityWest LafayetteUSA
  2. 2.Department of MathematicsUniversity of IllinoisUrbanaUSA

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