Journal of Applied Mathematics
Volume 2012 (2012), Article ID 701206, 8 pages
http://dx.doi.org/10.1155/2012/701206
Research Article

On Decomposable Measures Induced by Metrics

Dong Qiu1 and Weiquan Zhang2

1College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Nanan, Chongqing 400065, China
2School of Information Engineering, Guangdong Medical College, Guangdong, Dongguan 523808, China

Received 27 April 2012; Accepted 9 June 2012

Academic Editor: C. Conca

Copyright © 2012 Dong Qiu and Weiquan Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove that for a given normalized compact metric space it can induce a 𝜎 -max-superdecomposable measure, by constructing a Hausdorff pseudometric on its power set. We also prove that the restriction of this set function to the algebra of all measurable sets is a 𝜎 -max-decomposable measure. Finally we conclude this paper with two open problems.