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Abstract and Applied Analysis
Volume 2011, Article ID 867217, 9 pages
Research Article

A Note on the Generalized 𝑞 -Bernoulli Measures with Weight 𝛼

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

Received 21 April 2011; Accepted 16 May 2011

Academic Editor: Gabriel Turinici

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.


We discuss a new concept of the 𝑞 -extension of Bernoulli measure. From those measures, we derive some interesting properties on the generalized 𝑞 -Bernoulli numbers with weight 𝛼 attached to 𝜒 .