On the connection between hausdorff measures and capacity
On the connection between hausdorff measures and capacity
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论hausdorff测度与能力之间的联系
DOI：
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发表时间：
1958
期刊：
影响因子：
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通讯作者：
L. Carleson
中科院分区：
文献类型：
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作者：
L. Carleson
1.点集的度量刻画是沿着沿着两条不同的路线进行的。Hausdorff（1919）引入了现在称为I-Iausdorff测度的概念，容量的概念首先由Polya-Szeg（1931）给出了一般意义。[1] Frostman [3]（1935）给出了关于这两个概念之间联系的第一个一般性结果。他证明了，如果一个封闭集的容量为零，那么它的Hausdorff测度对每个递增函数h（r），h（0）= 0为零，使得
1. The metrical characterization of pointsets has been carried out along two different lines. Hausdorff (1919) introduced what is now called I-Iausdorff measures and the concept of capacity was first given a general sense by Polya-Szeg5 (1931). 1 The first general result on the connection between the two concepts was given by Frostman [3] (1935). He proved that if a closed set has capacity zero, then its Hausdorff measure vanishes for every increasing function h (r), h (0) = 0, such that