具有严格上维数测度的定义及等价定义

On the Definition and Equivalent Definitions of a Measure with Exact Upper Dimension

分形中严格上维数是与填充维数相关的一个概念,可以从不同的角度用三种方式来定义测度具有严格上维数,它们之间都是相互等价的。另一方面,测度具有严格上维数,一定具有相同的点维数,但反之不然。

Exact upper dimension is an associated definition of packing dimension, three definitions of measure with exact upper dimension from different approaches are given. Then it is proved that they are equivalent. On the other hand, It is attained that any measure with exact upper dimension is a measure with point dimension. But it is not the case for the converse.