FRACTAL DIMENSION: BOX DIMENSION, HAUSDORFF DIMENSION, AND POTENTIAL THEORY - ANESTASIA , MARIA
The concept of dimension has many aspects and meanings in mathematics, and there are a number of dierent denitions of the dimension of a set. In this thesis, 2 denitions of fractal dimension will be discussed, i.e. box-dimension and Hausdor dimension. The relation between box-dimension and Hausdor dimension, and methods to determine upper bound and lower bound of Hausdor dimension will also be studied. In the last part, examples of how to apply mass distribution principle and potential theory to determine the lower bound will be given on middle third Cantor set and Cantor dust.