Minkowski Content Analysis of Sierpinski Gasket and Von Koch Curve

In this paper, we study Minkowski contents of Sierpinski gasket and Von Koch curve. Some properties of two sets are given firstly. Then by adopting a new method, we calculate the upper Minkowski content and the lower Minkowski content of Sierpinski gasket respectively. We also deduce the good estimation formulae of Von Koch curve's upper Minkowski content and lower the lower Minkowski content. The results show that the upper Minkowski content is not equal to the lower Minkowski content in both kinds of sets. That is, their Minkowski contents do not exist and therefore are not Minkowski measurable.