A SUFFICIENT CONDITION FOR A BOUNDED SET OF POSITIVE LEBESGUE MEASURE IN R~2 OR R~3 TO CONTAIN ITS CENTROID

Eric A. Hintikka; Steven G. Krantz

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A SUFFICIENT CONDITION FOR A BOUNDED SET OF POSITIVE LEBESGUE MEASURE IN R~2 OR R~3 TO CONTAIN ITS CENTROID

机译：R〜2或R〜3中带正负数的Lebesgue度量的一个充要条件以包含其质心

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摘要

In this paper, we give a sufficient condition for a domain in either two- or three-dimensional Euclidean space to contain its centroid. We show that the condition is sharp. The condition is not, however, necessary.

机译：在本文中，我们为二维或三维欧氏空间中的一个域包含其质心提供了充分的条件。我们表明病情很严重。但是，该条件不是必需的。

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来源
《Real analysis exchange》 |2015年第1期|179-192|共14页
作者
Eric A. Hintikka; Steven G. Krantz;
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作者单位

Washington University in St. Louis;

Department of Mathematics, Washington University in St. Louis, St. Louis, Missouri 63130, USA;

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原文格式 PDF
正文语种 eng
中图分类
关键词
centroid; convex set; center of mass;

机译：质心凸集重心;

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2. On the cardinality and complexity of the set of codings for self-similar sets with positive Lebesgue measure [J] . Baker Simon Monatshefte fur Mathematik . 2016,第1期

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3. AN INFINITELY GENERATED SELF-SIMILAR SET WITH POSITIVE LEBESGUE MEASURE AND EMPTY INTERIOR [J] . Baker Simon, Sidorov Nikita Proceedings of the American Mathematical Society . 2019,第11期

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4. Necessary and Sufficient Conditions for Bounded Control of Positive Systems [C] . CHEN Junfei International Conference on Communications, Circuits and Systems Proceedings . 2008

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5. I. A necessary and sufficient condition that a curve lie on a quadric surface; II. A necessary and sufficient condition that a curve lie on a hyperquadric. [D] . Graue, Louis C. 1950

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7. On the cardinality and complexity of the set of codings for self-similar sets with positive Lebesgue measure [O] . Baker Simon 2016

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A SUFFICIENT CONDITION FOR A BOUNDED SET OF POSITIVE LEBESGUE MEASURE IN R~2 OR R~3 TO CONTAIN ITS CENTROID

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