完备度量空间上图定向自相似测度的局部维数

The Pointwise Dimension of Graph-directed Self-similar Measures in Complete Metric Spaces

运用遍历理论,讨论了完备度量空间上图定向自相似测度的局部维数,得出了dμ(x)=∑u∈V∑v∈Ve∑∈Euvλuρepvlogρe∑u∈V∑v∈Ve∑∈Euvλuρepvlogre关于测度μ对几乎所有的x∈K成立的结论.

In this paper, the pointwise dimension of graph-directed self-similar measures in complete metric spaces is investigated by Birkhoff ergodic theorem, and it comes to a conclusion that dμ（x）=∑u∈V ∑v∈V ∑e∈uvλuρePulog ρe/∑u∈V ∑v∈V ∑e∈uvλuρePulog γe about μ for almost every x∈K.