On the limits of generalization of the Kolmogorov integral

1. A. N. Kolmogorov, “Study of the notion of an integral,” in: Selected Works in Mathematics and Mechanics [in Russian], Moscow, 1985, pp. 96–136.

2. D. F. Goguadze, “On the relationship between the Kolmogorov and the Henstock integrals,” Mat. Zametki [Math. Notes], 60 (1996), no. 6, 832–844.

   Google Scholar 

3. R. Gordon, The Integrals of Lebesgue, Denjoy, Perron, and Henstock, Amer. Math. Soc., Providence, RI, 1994.

   Google Scholar 

4. N. Dunford and J. T. Schwartz, Linear Operators: General Theory, Interscience Publ., New York-London, 1958; Russian transl.: Inostr. Lit., Moscow, 1962.

   Google Scholar 

5. A. P. Solodov, “The integrals of Henstock and McShane for Banach-valued functions,” Mat. Zametki [Math. Notes], 65 (1999), no. 6, 860–870.

   Google Scholar 

6. A. Dvoretzky and C. A. Rogers, “Absolute and unconditional convergence in normed linear spaces,” Proc. Nat. Acad. Sci. USA, 36 (1950), no. 3, 192–197.

   Google Scholar 

7. J. Diestel and J. J. Uhl, Vector Measures, Amer. Math. Soc., Providence, RI, 1977.

   Google Scholar 

8. R. Gordon, “Another proof of the measurability of δ for the generalized Riemann integral,” Real Anal. Exchange, 15 (1989/90), 386–389.

   Google Scholar 

9. Genqian Liu, “The measurability of δ in Henstock integration,” Real Anal. Exchange, 13 (1987/88), 446–450.

   Google Scholar 

10. R. Gordon, “The McShane integration of Banach-valued functions,” Illinois J. Math., 34 (1990), 557–567.

    Google Scholar 

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