R^n上分形集多重维数的下界估计

On the lower bound of the multi-dimension of fractal sets on R^n

给出了Rn 上分形集多重维数的下界估计 .推广了Hausdorff测度的位势原理 :对分量均非负的向量α ,若有F上的具有有限α -能量的质量分布 ,则F的 (α)———维测度为无穷大 .利用位势原理证明了 :若有F上的具有有限α-能量的质量分布 ,则F的多重维数大于或等于α .

In this paper, we give a lower bound for the multi-dimension of fractal set on R n. Generating the principle of potential on Hausdorff measure, we shall establish a following theorem. Let α be a non-negative vector, if there is a quality distribution on F, α-energy of which is finite, then α-measure of F is infinite. We prove that under the condition above theorem the multi-dimension is larger than or equal to α.