DOI QR코드

DOI QR Code

A NOTE ON THE WEIGHTED LEBESGUE-RADON-NIKODYM THEOREM WITH RESPECT TO $p$-ADIC INVARIANT INTEGRAL ON $\mathbb{Z}_p$

  • Kim, Tae-Kyun (Division of General Education-Mathematics, Kwangwoon University) ;
  • Choi, Jong-Sung (Division of General Education-Mathematics, Kwangwoon University) ;
  • Kim, Hyun-Mee (Division of General Education-Mathematics, Kwangwoon University)
  • Received : 2011.09.25
  • Accepted : 2011.10.11
  • Published : 2012.01.30

Abstract

In this paper, we give the weighted Lebesgue-Radon-Nikodym theorem with respect to $p$-adic invariant integral on $\mathbb{Z}_p$.

Keywords

References

  1. J. M. Calabuig, P. Gregori, E.A Sanchez Perez, Radon-Nikodym derivative for vector measures belonging to Kothe function space, J. Math. Anal. Appl. 348(2008), 469-479. https://doi.org/10.1016/j.jmaa.2008.07.024
  2. K. George, On the Radon-Nikodym theorem, Amer. Math. Monthly. 115(2008), 556-558. https://doi.org/10.1080/00029890.2008.11920564
  3. T. Kim, Lebesgue-Radon-Nikodym theorem with respect to fermionic p-adic invariant measure on $\mathbb{Z}p$, Russ. J. Math. Phys. 19(2012), 00-00
  4. 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
  5. T. Kim, S.D. Kim, D.W. Park, On Uniformly differntiabitity and q-Mahler expansion, Adv. Stud. Contemp. Math. 4(2001), 35-41.
  6. T. Kim, Note on the Euler numbers and polynomials, Adv. Stud. Contemp. Math. 17(2008), 131-156.
  7. J. Choi, T.Kim, Y.H. Kim, A note on the q-analogues of Euler numbers and polynomials, to appear in Honam Math.
  8. 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