On the law of the iterated logarithm for continued fractions with sequentially restricted partial quotients

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