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Abstract:
The Ergodic Theorem serves as a link between dynamical systems and
random processes. In this lecture, we will illustrate the theorem by
developing a case study of continued fractions. As a corollary, we
will obtain the celebrated theorem of Khinchin: for "almost every"
positive irrational number x, the geometric means of the continued
fraction expansion of x converge to the limit K=2.6854520010653064453...
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