广义谢尔宾斯基海绵的Packing测度

The Packing Measure of the Generalized Sierpinski Sponge

中文关键词:  填充测度  自仿射集  谢尔宾斯斯海绵  维数

英文关键词:Packing measure  self-affine set  Sierpinski sponge  dimension

中文摘要:

      讨论了三维欧氏空间上的一类自仿射集──广义谢尔宾斯基(Sierpinski)海绵的填充测度(Packing Measure),对φ(t)=t^θ,φ(t)=t^θ/|logt|及更一般的情况,证明了填充测度P_ψ[K(T,D)]为无穷或有限的条件,

英文摘要:

      In this paper thc Packing measure of the generalized Sierpinski sponge of three-di-mension Euclidean space is discussed, For φ(t)=t^θ,φ(t)=t^θ/|logt| and genreal situations, the conditions that the Packing measure P_ψ[K(T,D)] is finite or infinite are proved,