S集的不可测性

Immeasurability of the Set S

指出了对于Rn中一些集合的Minkowski维数,已经得到了一些令人满意的结果,但是对于与此密切相关的Minkowski容度,所得到的结果还相当的不完善.通过自相似集合的分形性质准确地计算出了二维空间上S集的上Minkowski容度和下Minkowski容度,得到了它是Minkowski不可测的结果.

Some good results were already obtained for the Minkowski dimension of some sets in Rn.But some results of the Minkowski contents of the sets are not very perfect.This paper starts from the geometric properties of self-similar sets,obtains that the fractal set S is not Minkowski measurable by elementary methods.This method is accepted easily.