Kyungpook Mathematical Journal

  • 제52권3호
  • /
  • Pages.299-306
  • /
  • 2012
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지
DOI QR코드

DOI QR Code

A New Approach to the Lebesgue-Radon-Nikodym Theorem. with respect to Weighted p-adic Invariant Integral on ℤp

  • Rim, Seog-Hoon (Department of Mathematics Education, Kyungpook National University) ;
  • Jeong, Joo-Hee (Department of Mathematics Education, Kyungpook National University)
  • 투고 : 2012.07.09
  • 심사 : 2012.08.10
  • 발행 : 2012.09.23
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We will give a new proof of the Lebesgue-Radon-Nikodym theorem with respect to weighted p-adic q-measure on $Z_p$, using Mahler expansion of continuous functions, studied by the authors in 2012. In the special case, q = 1, we can derive the same result as in Kim, 2012, Kim et al, 2011.

키워드

참고문헌

  1. A. Bayad and T. Kim, Identities involving values of Bernstein, q-Bernoulli, and q- Euler polynomials. Russ. J. Math. Phys., 18(2)(2011), 133-143. https://doi.org/10.1134/S1061920811020014
  2. J. Choi, T. Kim and Y. H. Kim, A note on the q-analogues of Euler numbers and polynomials, to appear in Honam Math.
  3. T. Kim, q-Volkenborn integration. Russ. J. Math. Phys., 9(3)(2002), 288-299.
  4. T. Kim, Lebesgue-Radon-Nikodym theorem with respect to fermionic p-adic invariant measure on $Z_{p}$, Russ. J. Math. Phys., 19(2)(2012), 193-196 https://doi.org/10.1134/S1061920812020057
  5. T. Kim, Lebesgue-Radon-Nikodym theorem with respect to fermionic q-Volkenborn distribution on ${\mu}_{q}$, Appl. Math. Comp., 187(2007), 266-271. https://doi.org/10.1016/j.amc.2006.08.123
  6. T. Kim, A note on q-Bernstein polynomials. Russ. J. Math. Phys., 18(1)(2011), 73-82 https://doi.org/10.1134/S1061920811010080
  7. T. Kim, Note on the Euler numbers and polynomials, Adv. Stud. Contemp. Math., 17(2008), 131-156.
  8. T. Kim, Some identities on the q-Euler polynomials of higher order and q-Stirling numbers by the fermionic p-adic integral on $Z_{p}$, Russ. J. Math. Phys., 16(2009), 484-491. https://doi.org/10.1134/S1061920809040037
  9. T. Kim, New approach to q-Euler polynimials of higher order, Russ. J. Math. Phys., 17(2010), 218-225. https://doi.org/10.1134/S1061920810020068
  10. T. Kim, J. Choi and 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.
  11. T. Kim, D. V. Dolgy, S. H. Lee and C. S. Ryoo, Analogue of Lebesgue-Radon-Nikodym theorem with respect to p-adic q-measure on $Z_{p}$, Abstract and Applied Analysis, 2011(2011), Article ID637634, 6 pages.
  12. T. Kim, S. D. Kim and D. W. Park,, On Uniformly differntiabitity and q-Mahler expansion, Adv. Stud. Contemp. Math., 4(2001), 35-41.
  13. J. Jeong and S.-H. Rim, A Note on the Lebesgue-Radon-Nikidym Theorem with respect to Weighted p-adic Invariant Integral on $Z_{p}$, Abstract and Applied Analysis, 2012(2012), Article ID 696720, 8pages