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On Some Criteria for a Set to be of Class N

Published online by Cambridge University Press:  22 January 2016

Nobuyuki Suita
Nobuyuki Suita*
Affiliation:
Department of Mathematics, Tokyo Metropolitan University
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Let D be a plane domain containing the point at infinity and E its complementary closed set. As to a sufficient condition for a compact set E to be of class N, Pfluger-Mori’s criterion is well-known (Pfluger [10], Mori [6]). Various relations between the conditions of this type and the Hausdorff measure of the set E have been investigated recently by Kuroda and Ozawa (Kuroda [5], Ozawa and Kuroda [8], Ozawa [7]). For example they showed that Pfluger-Mori’s condition implies that the set E is of one dimensional measure zero under some additional conditions (cf. [7], [8]). In the present paper we shall give an alternative proof of Pfluger-Mori’s criterion and another criterion using analytic module and, further, prove some criteria for the set E to be of one dimensional measure zero.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 19 , October 1961 , pp. 189 - 194
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1961

References

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