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Some applications of a theorem of Marcinkiewicz

Part of the Lecture Notes in Mathematics book series (LNM,volume 1419)

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Bibliography

  1. H. Bauer. Der Perronsche Integralbegriff und seine Beziehung zum Lebesgueschen, Monatsh. Math. Phys., 26(1915), 153–198.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. A. Bruckner. Differentiation of Real Functions, Lecture Notes in Math., #659 Berlin-Heidelberg-New York, 1978.

    Google Scholar 

  3. P.S. Bullen. The Burkill approximately continuous integral, J. Austral. Math. Soc., (Ser. A)35 (1983), 236–253.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. . The Burkill approximately continuous integral II, Math. Chron., 12(1983), 93–98.

    MathSciNet  MATH  Google Scholar 

  5. P.S. Bullen and R. Vyborny. Some applications of a theorem of Marcinkiewicz, to appear, Canad. Math. Bull.

    Google Scholar 

  6. J.C. Burkill. The approximately continuous Perron integral, Math. Z., 34 (1931), 270–278.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. V.G. Celidze and A.G. Dzvarseisvili. Teoriya Integrala Denjoy i Nekotorye eë Prilozeniya, Tbilis. Gos. Univ., Tbilis, 1978. Engl. transl. to appear.

    Google Scholar 

  8. Chew, T.-S. On the generalized dominated convergence theorem, Bull. Austral. Math. Soc., 37(1980), 165–171.

    MathSciNet  MATH  Google Scholar 

  9. E.A. Coddington. Theory of Ordinary Differential Equations, New York, 1955.

    Google Scholar 

  10. A. Denjoy. Leçons sur le Calcul de Coefficients d'une Série Trigonométrique, Vol. IV.2, Paris, 1949.

    Google Scholar 

  11. R. Henstock. Theory of Integration, London, 1963.

    Google Scholar 

  12. Y. Kubota. A characterization of the approximately continuous Denjoy integral, Canad. J. Math., 22(1970), 219–226.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. J. Kurzweil. Nichtabsolut Konvergente Integrale, Leipzig, 1980.

    Google Scholar 

  14. Lee P.-Y. and Chew T.-S. On convergence theorems for non-absolute integrals, Bull. Austral. Math. Soc., 34(1986), 133–140.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Lee P.-Y. and Lu S. Notes on Classical Integration Theory (VIII), Res. Rep. #324, Dept. Math., National Univ. Singapore, 1988.

    Google Scholar 

  16. E.W. McShane. On Perron integration, Bull. Amer. Math. Soc., 48(1942), 718–726.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. I.P. Natanson. Theory of Functions of a Real Variable, Vol. I, Engl. transl. (2nd ed. rev.), New York, 1961.

    Google Scholar 

  18. O. Perron. Über den Integralbegriff, Sitzber. Heidleberg Akad. Wiss. Abt. A, 16(1914), 1–16.

    MATH  Google Scholar 

  19. J. Ridder. Über approximativ stetiger Denjoy-Integrale, Fund. Math., 21 (1933), 1–10.

    MATH  Google Scholar 

  20. . Ueber Definitionen von Perron-Integralen I, II, Indag. Math., 9(1947), 227–235, 280–289.

    MATH  Google Scholar 

  21. S.Saks. Theory of the Integral, 2nd ed. rev., New York, 1937.

    Google Scholar 

  22. D.N. Sarkhel. A criterion for Perron integrability, Proc. Amer. Math. Soc., 7(1978), 109–112.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. A.W. Schurle. A function is Perron integrable if it has locally small Riemann sums, J. Austral. Math. Soc., (Ser. A)36(1986), 220–232.

    MathSciNet  MATH  Google Scholar 

  24. V.A. Skvorcov. Some properties of CP-integrals, Amer. Math. Soc. Transl., (2)54(1966), 231–254.

    CrossRef  Google Scholar 

  25. G. Tolstov. Sur l'intégrale de Perron, Math. Sb., 5(1939), 647–660.

    MATH  Google Scholar 

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© 1990 Springer-Verlag

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Bullen, P.S. (1990). Some applications of a theorem of Marcinkiewicz. In: Bullen, P.S., Lee, P.Y., Mawhin, J.L., Muldowney, P., Pfeffer, W.F. (eds) New Integrals. Lecture Notes in Mathematics, vol 1419. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083095

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  • DOI: https://doi.org/10.1007/BFb0083095

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