Hausdorff Measure Of Generalized Cantor Set

Firstly , this paper discusses the fractal set with its characteristics and gives the definition of the fractal set by characteristics .It also discusses the different definition of fractal dimensions and their corresponding properties. It proves the relations between measure and dimension, dimension and dimension .The results can be used depict the degree of "thickness" for a fractal set and provide a basis for understanding and applying fractal dimension, and also, the results may clarify some mistake knowledge about fractal dimension, such that one can see the fact - a fractal set may have different values of dimension under different definitions of dimensions, and the different values of dimensions character different attributes of the fractal set. Secondly, this paper tell us about Iterated Function System,f = {f₁,f₂,…,f-k) .definite f(E) =(i=1)|(U|k)fi(E), fi(i= 1,2,…,k), f⁰(E)=E, fⁿ (E) =...