Joo-Hee Jeong, Jin-Woo Park, Seog-Hoon Rim and Joung-Hee Jin

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 21, 2015, Number 1, Pages 10—17

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## Details

### Authors and affiliations

Joo-Hee Jeong

*Department of Mathematics Education, Kyungpook National University
Taegu 702-701, Republic of Korea*

Jin-Woo Park

*Department of Mathematics Education, Sehan University
YoungAm-gun, Chunnam, 526-702, Republic of Korea*

Seog-Hoon Rim

*Department of Mathematics Education, Kyungpook National University
Taegu 702-701, Republic of Korea*

Joung-Hee Jin

*Department of Mathematics Education, Kyungpook National University
Taegu 702-701, Republic of Korea*

### Abstract

In this paper we will give the Lebesgue–Radon–Nikodym theorem with respect to weighted and twisted *p*-adic *q*-measure on ℤ_{p}. In special case, if there is no twisted, then we can derive the same result as Jeong and Rim, 2012; If the case weight zero and no twist, then we derive the same result as Kim 2012.

### Keywords

*p*-adic invariant integral*p*-adic*q*-measure- Lebesgue–Radon–Nikodym theorem

### AMS Classification

- 11B68
- 11S80

### References

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- Jeong, J. & S. H. Rim. (2012) A note on the Lebesgue–Radon–Nikodym theorem with respect to weighted p-adic invariant integral on Z
_{p}, Abstract and Applied Analysis, 2012, Article ID 696720, 8 pages. - Kim, T. (2002) q-Volkenborn integration. Russ. J. Math. Phys. 9(3), 288–299.
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- Kim, T., J. Choi & H. Kim A note on the weighted Lebesgue–Radon–Nikodym theorem with respect to p-adic invariant integral on Z
_{p}. to appear in JAMI. - Kim, T., D. V. Dolgy, S. H. Lee & C. S. Ryoo. (2011) Analogue of Lebesgue–Radon–Nikodym theorem with respect to p-adic q-measure on Z
_{p}. Abstract and Applied Analysis, 2011, Article ID637634, 6 pages. - Kim, T., S. D. Kim, & D. W. Park. (2001) On Uniformly differntiabitity and q-Mahler expansion. Adv. Stud. Contemp. Math., 4, 35–41.
- Kim, Y. H., B. Lee & T. Kim. (2011) On the q-extension of the twisted generalized Euler numbers and polynomials attached to χ. J. of Comp. Anal. and Appl., 13(7), 1208–1213.
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## Cite this paper

APAJeong, J.-H., Park, J.-W., Rim, S.-H., & Jin, J.-H. (2015). A note on the Lebesgue–Radon–Nikodym theorem with respect to weighted and twisted *p*-adic invariant integral on ℤ_{p}. Notes on Number Theory and Discrete Mathematics, 21(1), 10-17.

Jeong, Joo-Hee, Jin-Woo Park, Seog-Hoon Rim and Joung-Hee Jin. “A Note on the Lebesgue–Radon–Nikodym Theorem with Respect to Weighted and Twisted *p*-adic Invariant Integral on ℤ_{p}.” Notes on Number Theory and Discrete Mathematics 21, no. 1 (2015): 10-17.

Jeong, Joo-Hee, Jin-Woo Park, Seog-Hoon Rim and Joung-Hee Jin. “A Note on the Lebesgue–Radon–Nikodym Theorem with Respect to Weighted and Twisted *p*-adic Invariant Integral on ℤ_{p}.” Notes on Number Theory and Discrete Mathematics 21.1 (2015): 10-17.. Print.