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The ap-Denjoy Integral of Banach-valued Functions

김영국|김병무|박재명
한국수학교육학회|2008.08|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제15권 제3호|pp. 343-351

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참고문헌

키워드

Denjoy integralapproximate Lusin functionap-Denjoy integral.
주제분류수학

초록

In this paper, we define the Denjoy and ap-Denjoy integrals of Banach- valued functions, and we investigate some properties of these two integrals. In particular, we show that a Denjoy integrable function is ap-Denjoy integrable.

Abstract

In this paper, we define the Denjoy and ap-Denjoy integrals of Banach- valued functions, and we investigate some properties of these two integrals. In particular, we show that a Denjoy integrable function is ap-Denjoy integrable.

참고문헌 (15)

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  3. R.A. Gordon, "Some comments on the McShane and Henstock integrals", Real Anal. Exch, 23, pp.329~341 (1997)
  4. "The integrals of Lebesgue, Denjoy, Perron and Henstock", Amer. Math. Soc. Providence, ~ (1994)
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  6. J. Kurzweil, "Perron type integration on n-dimensional intervals as an extension of intergration of step funcions by strong equiconvergence", Czechoslovak Math. J, 46(121), pp.1~20 (1996)
  7. T.Y. Lee, "On a generalized dominated convergence theorem for the AP-integral", Real Anal. Exch, 20, pp.77~88 (1995)
  8. K. Liao, "On the descriptive definition of the Burkill approximately continuous integral", Real. Anal. Exch, 18, pp.253~260 (1993)
  9. Y.J. Lin, "On the equivalence of four convergence theorems for the AP-integral", Real Anal. Exch, 19, pp.155~164 (1994)
  10. J.M. Park, "Bounded convergence theorem and integral operator for operator valued measures", Czechoslovak Math. J, 47(122), pp.425~430 (1997)
  11. :The Denjoy extension of the Riemann and McShane integrals.Czechoslovak Math.J.50, "The Denjoy extension of the Riemann and McShane integrals", Czechoslovak Math. J, 50(125), pp.615~625 (2000)
  12. J.M. Park, "The s-Perron, sap-Perron and ap-McShane integrals", Czechoslovak Math. J, 54(129), pp.545~557 (2004)
  13. J.M. Park, "The ap-Denjoy and ap-Henstock integrals", Czechoslovak Math. J, 57(132), pp.689~696 (2007)
  14. A.M. Russell, "Stieltjes type integrals", J. Austral. Math. Soc(Ser. A), 20, pp.431~448 (1975)
  15. "A Banach space of functions of generalized variation", Bull. Aust. Math. Soc, 15, pp.431~438 (1975)

관련 논문AI추천

The Denjoy*-Stieltjes Extension of the Bochner, Dunford, Pettis and McShane Integrals박춘기, 오미나한국수학교육학회 · 이론수학과 교직수학2008 · 제15권 제3호Some properties of the ap-Denjoy Integral김영국, 박재명, 윤주한대한수학회 · 대한수학회보2005 · 제42권 제3호Convergence theorems for Denjoy-Pettis integrable fuzzy mappings박춘기강원경기수학회 · 한국수학논문집2010 · 제18권 제3호Convergence theorems for set-valued Denjoy-Pettis integrable mappingsChun-Kee Park대한수학회 · 대한수학회논문집2009 · 제24권 제2호ON DENJOY*-STIELTJES INTEGRAL박춘기, 오미나강원경기수학회 · 한국수학논문집2008 · 제16권 제4호On Henstock integral of fuzzy mappings in Banach spaces박춘기, 오미영강원경기수학회 · 한국수학논문집2009 · 제17권 제3호

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