有限型子转移对Hausdorff测度保测的充要条件

A Full and Necessary Condition for the Subshift of Finite Type is a Measure-Preserving Transformation with Respest to the Hausdorff Measure

本文讨论了N个符号组成的（单边）符号空间中由N×N0，1-矩阵A所决定的有限型号转移(ΣA,σA）．给出了当时，σA是测度空间上保测变换的一个充要条件．s表示ΣA的Hausdorff维数，表示ΣA上的s-维Hausdorff测度，表示ΣA中一切Borel子集所构成的σ-代数．

In this paper,the subshift of finite boe (ΣA, σA) determined by tile N×N 0,1 - matrix A on theone-sided symbolic space ΣA of N - symbol is discussed.It is shown that a full and necessarycondition for the σA is a measure-preserving trailsformation on the measure space ifWhere s is the Hausdorff dimension of ΣA , denotes the Hausdorff s - dimensionalmeasure on ΣA and is the σ - algebra of borel subsets of ΣA.