Real Analysis Exchange

A Sufficient Condition for a Bounded Set of Positive Lebesgue Measure in ℝ 2 or ℝ 3 to Contain its Centroid

Eric A. Hintikka and Steven G. Krantz

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Abstract

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.

Article information

Source
Real Anal. Exchange, Volume 40, Number 1 (2015), 179-192.

Dates
First available in Project Euclid: 1 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.rae/1435759202

Mathematical Reviews number (MathSciNet)
MR3365397

Subjects
Primary: 51M04: Elementary problems in Euclidean geometries
Secondary: 26E99: None of the above, but in this section

Keywords
centroid convex set center of mass

Citation

Hintikka, Eric A.; Krantz, Steven G. A Sufficient Condition for a Bounded Set of Positive Lebesgue Measure in ℝ 2 or ℝ 3 to Contain its Centroid. Real Anal. Exchange 40 (2015), no. 1, 179--192. https://projecteuclid.org/euclid.rae/1435759202


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