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.

中文翻译：

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关于具有连续受限部分商的连续分数的迭代对数定律

我们为实数集，其建立的重对数（LIL）的法律Ñ个部分商比更大α _Ñ，其中（α _Ñ）是一个序列，使得Σ1/ α _Ñ是有限的。在许多情况下，该集合的Hausdorff尺寸为1/2，而LIL中的尺寸与Hausdorff尺寸绝对是连续的。通过对顺序迭代函数系统的极限集上的无界可观测变量应用强不变性原理获得结果。