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General integration and extensions.II
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 4, pp. 983-1005 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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This work is a continuation of the paper (Š. Schwabik: General integration and extensions I, Czechoslovak Math.\ J. 60 (2010), 961--981). Two new general extensions are introduced and studied in the class $\frak T$ of general integrals. The new extensions lead to approximate description of the Kurzweil-Henstock integral based on the Lebesgue integral close to the results of S. Nakanishi presented in the paper (S. Nakanishi: A new definition of the Denjoy's special integral by the method of successive approximation, Math.\ Jap. 41 (1995), 217--230).
This work is a continuation of the paper (Š. Schwabik: General integration and extensions I, Czechoslovak Math.\ J. 60 (2010), 961--981). Two new general extensions are introduced and studied in the class $\frak T$ of general integrals. The new extensions lead to approximate description of the Kurzweil-Henstock integral based on the Lebesgue integral close to the results of S. Nakanishi presented in the paper (S. Nakanishi: A new definition of the Denjoy's special integral by the method of successive approximation, Math.\ Jap. 41 (1995), 217--230).
Classification : 26A39, 26A42
Keywords: abstract integration; extension of integral; Kurzweil-Henstock integration 
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Schwabik, Štefan. General integration and extensions.II. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 4, pp. 983-1005. http://geodesic.mathdoc.fr/item/CMJ_2010_60_4_a7/

[1] Bongiorno, B., Piazza, L. Di, Skvortsov, V.: A new full descriptive characterization of Denjoy-Perron integral. Real Anal. Exch. 21 (1995), 656-663. | DOI | MR | Zbl

[2] Foran, J.: Fundamentals of Real Analysis. Marcel Dekker New York (1991). | MR | Zbl

[3] Gordon, R. A.: The Integrals of Lebesgue, Denjoy, Perron and Henstock. American Mathematical Society Providence (1994). | MR | Zbl

[4] Kubota, Y.: Abstract treatment of integration. Math. J. Ibaraki Univ. 29 (1997), 41-54. | DOI | MR | Zbl

[5] Kurzweil, J.: Nichtabsolut konvergente Integrale. BSB B. G. Teubner Verlagsgesellschaft Leipzig (1980). | MR | Zbl

[6] Lee, P.-Y.: Lanzhou Lectures on Henstock Integration. World Scientific Singapore (1989). | MR | Zbl

[7] Lee, P.-Y., Výborný, R.: The Integral; An Easy Approach after Kurzweil and Henstock. Cambridge Univ. Press Cambridge (2000). | MR

[8] Nakanishi, S.: A new definition of the Denjoy's special integral by the method of successive approximation. Math. Jap. 41 (1995), 217-230. | MR | Zbl

[9] Saks, S.: Theory of the Integral. Hafner New York (1937). | Zbl

[10] Schwabik, Š.: Variational measures and the Kurzweil-Henstock integral. Math. Slovaca 59 (2009), 731-752. | DOI | MR

[11] Schwabik, Š.: General integration and extensions I. Czech. Math. J. 60 (2010), 961-981. | DOI | MR

[12] Thomson, B. S.: Derivates of Interval Functions. Mem. Am. Math. Soc. 452 (1991). | MR | Zbl