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Keywords:
McShane’s partition; Kurzweil-Henstock’s partition
McShane’s partition; Kurzweil-Henstock’s partition
Summary:
Riemann-type definitions of the Riemann improper integral and of the Lebesgue improper integral are obtained from McShane’s definition of the Lebesgue integral by imposing a Kurzweil-Henstock’s condition on McShane’s partitions.
References:
[1] B. Bongiorno: Un nuovo integrale per il problema delle primitive. Le Matematiche 51 (1996), 299–313.
[2] B. Bongiorno, L. Di Piazza and D. Preiss: A constructive minimal integral which includes Lebesgue integrable functions and derivatives. J. London Math. Soc. 62 (2000), 117–126. DOI 10.1112/S0024610700008905 | MR 1771855
[3] A. M. Bruckner, R. J. Fleissner and J. Foran: The minimal integral which includes Lebesgue integrable functions and derivatives. Coll. Math. 50 (1986), 289–293. DOI 10.4064/cm-50-2-289-293 | MR 0857865
[4] R. A. Gordon: The Integrals of Lebesgue, Denjoy, Perron, and Lebesgue. Graduate Studies in Math. vol. 4, AMS, 1994. MR 1288751
[5] E. J. McShane: A unified theory of integration. Amer. Math. Monthly 80 (1973), 349–359. DOI 10.2307/2319078 | MR 0318434 | Zbl 0266.26008
[6] K. Kurzweil: Nichtabsolut Konvergente Integrale. Teubner, Leipzig, 1980. MR 0597703 | Zbl 0441.28001
[7] W. F. Pfeffer: The Riemann Approach to Integration. Cambridge Univ. Press, Cambridge, 1993. MR 1268404 | Zbl 0804.26005
[8] S. Saks: Theory of the Integral. Dover, New York, 1964. MR 0167578
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