The distribution of partial quotients in the simple continued fraction expansion of a real number Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/f7623h20x

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  • By using continued fractions the set of positive irrationals can be put in one to one correspondence with the set of sequences of positive integers. The entries of an arbitrary sequence of integers can be any subset of Z and each integer appearing can occur once, infinitly often, or anything in between. Using the standard Lebesgue measure this paper shows for almost every real the corresponding sequence has every integer occurring infinitly often. This and related topics are derived for the irrationals. Analogous results are discussed for the rationals.
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