Applications of the Birkhoff Ergodic Theorem
نویسنده
چکیده
Ergodic theory studies the long-term averaging properties of measurepreserving dynamical systems. In this paper, we state and present a proof of the ergodic theorem due to George Birkhoff, who observed the asymptotic equivalence of the time-average and space-average of a point x in a finite measure space. Then, we examine a number of applications of this theorem in number-theoretic problems, including a study of normal numbers and of Lüroth series transformations.
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