A Study On Some Metric Properties Of A Class Of Staggered Expansions

In this thesis,we study some metric properties of staggered expansions in real number field,and the results are more general.The research content of this paper is divided into three parts In the first part,we mainly study the " 0-1" law of ?-Lüroth expansion numbers.The upper bound of a set is estimated by defining a measurable set covering the upper bound of the set,which is similar to the LüRoth expansion,which constructs a subset of the set and establishes the symbol space to calculate the dimension of the subset.Get results:For almost all x?(0,1),(?) here,Ln(x)=max{l1(x),l2(x),?,ln(x)}.In the second part,according to Borel Bernstein Theorem,a set of zero Lebesgue measures is defined.The results are as follows:The Hausdorff dimension result of set F?={x?(0,l]:ln(x)??(n),i.o.n} is dimH F?=0,where ? is the integer value function defined on n,and it satisfies the following:when n??,?(n)??.In the third part,we mainly study the Hausdorff dimension result of the maximum number exception set.The results are as follows:For any ??0,the Hausdorff dimension of(?) is obtained.Hausdorff dimension result of:dimH E(?)=1.