Category and dimensions for cut-out sets
The authors study the modified box dimension of cut-out sets that belong to a positive, nonincreasing and summable sequence. By noting that the family of this kind of sets is a compact metric space under the Hausdorff metric, the authors prove that the lower modified box dimension equals to zero and the upper modified box dimension equals to the upper box dimension for almost all cut-out sets in the sense of Baire category.
scientific article; zbMATH DE number 5577099