The fractional dimensional theory of continued fractions
The fractional dimensional theory of continued fractions
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DOI：
10.1017/s030500410002171x
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发表时间：
1941-07
影响因子：
0.8
通讯作者：
I. Good
中科院分区：
文献类型：
--
作者：
I. Good
分数维的概念现在已经很有名了。本文的目的是研究点集的维数，当这些点集被表示为连分式时，它们的部分商服从一些简单的限制。所考虑的集合自然是线性测度为0的。这些对几乎所有连分式都成立的部分商的性质构成了Khintchine所称的“连分式的测度理论”。
The notion of fractional dimensions is one which is now well known. The object of the present paper is the investigation of the dimensional numbers of sets of points which, when expressed as continued fractions, obey some simple restriction as to their partial quotients. The sets considered are naturally of linear measure zero. Those properties of the partial quotients which hold for almost all continued fractions make up the subject called by Khintchine ‘the measure theory of continued fractions’.