Abstract and Applied Analysis
Volume 2011 (2011), Article ID 637634, 7 pages
http://dx.doi.org/10.1155/2011/637634
Research Article

Analogue of Lebesgue-Radon-Nikodym Theorem with respect to 𝑝 -adic 𝑞 -Measure on ℤ 𝑝

T. Kim,1 D. V. Dolgy,2 S. H. Lee,3 and C. S. Ryoo4

1Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
2Hanrimwon, Kwangwoon University, Seoul 139-701, Republic of Korea
3Division of General Education, Kwangwoon University, Seoul 139-701, Republic of Korea
4Department of Mathematics, Hannam University, Daejeon 306-791, Republic of Korea

Received 3 July 2011; Accepted 12 August 2011

Academic Editor: H. B. Thompson

Copyright © 2011 T. Kim et al. 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

Recently, Lebesgue-Radon-Nikodym theorem with respect to fermionic 𝑝 -adic invariant measure on ℤ 𝑝 was studied in Kim. In this paper we will give the analogue of the Lebesgue-Radon-Nikodym theorem with respect to 𝑝 -adic 𝑞 -measure on ℤ 𝑝 . In special case, 𝑞 = 1 , we can derive the same results in Kim.