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タイトルヨミ
サシュウゴウ ノ ハウスドルフ ジゲン ニ ツイテ ノ チュウイ
タイトル別表記
Notes on Fractional Dimensions of Difference Sets
ファイル
言語
英語
著者
秦野 薫
内容記述(抄録等)
Under the continuum hypothesis W. Sierpinski [7] proved that a set E which possesses 'the property C' is of measure zero with respect to any Hausdorff measure but E-E=R^1. In his proof we can see that a difference set A-B is closely related to the orthogonal projection of the product set A×B in the xy-plane to the line y= -x. In [8] D. J. Ward defined an n-difference set D^r(E) of a non empty set E⊂R^1 and showed that dim D (E)≦min {nα, n-1} under the conditions that the set E is an α-set and it has positive lower density with respect to the α-dimensional Hausdorff measure at every point in it.
In this iemark we shall estimate the lower and upper bounds of fractional dimensions of difference sets and show that the upper bound is sharp.
In §1, following [4] we shall define a perfect set of translation and under some condition we shall evaluate the Hausdorff measure of it in §2. In §3 we shall discuss the fractional dimensions of difference sets.
掲載誌名
島根大学教育学部紀要. 自然科学
13
開始ページ
1
終了ページ
9
ISSN
05869943
発行日
1979-12-25
NCID
AN00107941
出版者
島根大学教育学部
出版者別表記
The Faculty of Education Shimane University
資料タイプ
紀要論文
部局
教育学部
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