We study the metrical theory of fibred systems, in particular, in the case of continued fraction mixing systems. We get the limit distribution of the largest value of a continued fraction mixing stationary stochastic process with infinite expectation and some related results. These are analogous to J. Galambos, W. Philipp, and H. G. Diamond-J. D. Vaaler theorems for the regular continued fractions. As an application, we see that these theorems hold for Jacobi-Petron algorithm.
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