中文摘要：

作为具有严格自相似性的经典分形集,Sierpinski垫是估算Hausdorff维数及Hausdorff测度时最主要的首选研究对象。在估算Hausdorff维数及Hausdorff测度时,许多文献采用特殊三角形构造Sierpinski垫。在任意三角形上构造了Sierpinski垫,并通过投影定理估算出了其Hausdorff测度的上下界。

英文摘要：

As one of classical rigorous self-similarity fractal sets,Sierpinski carpet is the main object when people estimate the Hausdorff dimension and the Hausdorff measure.In estimating the Hausdorff dimension and the Hausdorff measure,many literatures construct Sierpinski carpet by special triangles.Sierpinski carpet is first constructed on arbitrary triangle,and then lower bound and upper bound of its Hausdorff measure is estimated via projection theorem.