Hausdorff Measure And The Mass Distribution Principle For The Self-Similar Sets And Applications

In this paper, seven equivalent criterions about Hausdorff measure for the Self--similar sets satisfying the open set condition has been given and we give a detail proof. We use the mass distribution principle for the self-similar sets satisfying the open set condition and obtain a new method for computing the exact value of the Hausdorff measure for a class of self-similar sets satisfying the open set condition. We give some examples to explain this method, compute the exact value of the Hausdorff measure for a class of Cantor sets.