The Box Dimension Of Sierpinski Carpet Of High Dimension With Gap Sequence

In this paper,we proved the upper box dimension of the compact set E of R is determined by the gap sequence of E according to the generation of the definition of gap sequence by Hui Rao etc.Then we created a cover of the high dimension sierpinski carpet,of which the lebesgue measure of the connected components satisfied certain condition such that the upper box dimension of the compact set E can be determined by the gap sequence.