Open Access
2007/2008 The Median of a Continuous Function
Sunny Garlang Noah
Real Anal. Exchange 33(1): 275-280 (2007/2008).


Let $\Omega $ be a domain in $\mathbb{R}^{n}$ with finite Lebesgue measure and $f\in C\left( \Omega \right) \cap L^{1}\left( \Omega \right) $ a real-valued function on $\Omega $. It is shown that there exists a unique number $M\in \mathbb{R}$ at which the function $I\left( y\right) =\int_{\Omega }\left| f\left( x\right) -y\right| d\lambda ^{n}\left( x\right) $ is minimized, where $\lambda ^{n}$ is the Lebesgue measure on $% \mathbb{R}^{n}$. We can define this number as \textit{the }median of $f$ over $\Omega $ with respect to $\lambda ^{n}$.


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Sunny Garlang Noah. "The Median of a Continuous Function." Real Anal. Exchange 33 (1) 275 - 280, 2007/2008.


Published: 2007/2008
First available in Project Euclid: 28 April 2008

MathSciNet: MR2402879
zbMATH: 1142.60005

Primary: 26D15 , 60A10

Keywords: Continuous function , median

Rights: Copyright © 2007 Michigan State University Press

Vol.33 • No. 1 • 2007/2008
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