A note on the Lebesgue–Radon–Nikodym theorem with respect to weighted and twisted p-adic invariant integral on ℤp

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
Full paper (PDF, 129 Kb)

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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 ℤp. 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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  4. George, K. (2008) On the Radon–Nikodym theorem, Amer. Math. Monthly, 115, 556–558.
  5. Jeong, J. & S. H. Rim. (2012) A note on the Lebesgue–Radon–Nikodym theorem with respect to weighted p-adic invariant integral on Zp, Abstract and Applied Analysis, 2012, Article ID 696720, 8 pages.
  6. Kim, T. (2002) q-Volkenborn integration. Russ. J. Math. Phys. 9(3), 288–299.
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  17. Jeong, J. & S. H. Rim. (2012) A note on the Lebesgue–Radon–Nikodym theorem with respect to weighted p-adic invariant integral on Zp. Abstract and Applied Analysis, 2012, Article ID 696720, 8 pages.

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Cite this paper

Jeong, 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 ℤp. Notes on Number Theory and Discrete Mathematics, 21(1), 10-17.

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