Abstract
We establish a law of the iterated logarithm (LIL) for the set of real numbers whose nth partial quotient is bigger than α n , where (α n ) is a sequence such that ∑1/α n is finite. This set is shown to have Hausdorff dimension 1/2 in many cases and the measure in LIL is absolutely continuous to the Hausdorff measure. The result is obtained as an application of a strong invariance principle for unbounded observables on the limit set of a sequential iterated function system.
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