Additive functions of intervals and Hausdorff measure
Additive functions of intervals and Hausdorff measure
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DOI：
10.1017/s0305004100022684
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发表时间：
1946-02
影响因子：
0.8
通讯作者：
P. Moran
中科院分区：
文献类型：
--
作者：
P. Moran
考虑Q尺寸的欧几里得空间RQ中的有界点。让H（t）是连续增加的函数，呈t> 0，因此H（0）= 0。相对于函数h（t）的集合e定义为以下内容。直径di小于或等于ε
Consider bounded sets of points in a Euclidean space Rq of q dimensions. Let h(t) be a continuous increasing function, positive for t>0, and such that h(0) = 0. Then the Hausdroff measure h–mE of a set E in Rq, relative to the function h(t), is defined as follows. Let ε be a small positive number and suppose E is covered by a finite or enumerably infinite sequence of convex sets {Ui} (open or closed) of diameters di less than or equal to ε. Write h–mεE = greatest lower bound for any such sequence {Ui}. Then h–mεE is non-decreasing as ε tends to zero. We define