乘积概率空间中的密度定理

Density Theorems in Product Probability Spaces

密度定理是分形理论中非常重要的定理,Dai Chaoshou和Taylor S J在文献[1]中给出了概率空间中的密度定理.本文推广了文献[1]中的结果,在乘积概率空间中证明了相应于Hausdorff测度与Packing测度的密度定理.

In fractals theory,the density theorems are very important. In Ref. [1] the density theorems have been proved in probability spaces by Dai Chaoshou and Taylor S J. In this paper,the density theorems in product probability spaces are studied,and the density theorems about Hausdorff measures and Packing measures are obtained, respectively.