一般Sierpienski地毯的全豪斯多夫维数的测度
Measures of the full Hausdorff dimension for a general Sierpiński carpet
摘要：
研究了一般Sierpienski地毯的满尺寸的度量。在本文的第一部分中，我们给出了Sierpienski地毯的全豪斯多夫维数的一个度量准则。同时，它是零势关于矩阵值势$α\mathbf{N}$（稍后定义）的某个Gibbs测度$ν_α$的条件平衡测度。一方面，在没有条件\textbf{(H)}的情况下推广了[17]的结果.另一方面，它提供了一个可检验的条件来保证一般Sierpienski地毯的全豪斯多夫维数测度的存在唯一性.本文的第二部分给出了马氏投影测度的一个判别准则，并利用导出的矩阵值位势估计了它的步数。这些结果使我们能够回答[1]和[4]中关于投影测度和因子的一些问题。
英文摘要：
The measure of the full dimension for a general Sierpiński carpet is studied. In the first part of this study, we give a criterion for the measure of the full Hausdorff dimension of a Sierpiński carpet. Meanwhile, it is the conditional equilibrium measure of zero potential with respect to some Gibbs measure $ν_α$ of matrix-valued potential $α\mathbf{N}$ (defined later). On one hand, this investigation extends the result of [17] without condition \textbf{(H)}. On the other hand, it provides a checkable condition to ensure the existence and uniqueness of the measure of the full Hausdorff dimension for a general Sierpiński carpet. In the second part of this paper we give a criterion for the Markov projection measure and estimate its number of steps by means of the induced matrix-valued potential. The results enable us to answer some questions which arise from [1] and [4] on the projection measure and factors.
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