Abstract
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.
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References
B. Bongiorno: Un nuovo integrale per il problema delle primitive. Le Matematiche 51 (1996), 299-313.
B. Bongiorno, L. Di Piazza and D. Preiss: A constructive minimal integral which in-cludes Lebesgue integrable functions and derivatives. J. London Math. Soc. 62 (2000), 117-126.
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.
R. A. Gordon: The Integrals of Lebesgue, Denjoy, Perron, and Lebesgue. Graduate Studies in Math. vol. 4, AMS, 1994.
E. J. McShane: A unified theory of integration. Amer. Math. Monthly 80 (1973), 349-359.
K. Kurzweil: Nichtabsolut Konvergente Integrale. Teubner, Leipzig, 1980.
W. F. Pfeffer: The Riemann Approach to Integration. Cambridge Univ. Press, Cam-bridge, 1993.
S. Saks: Theory of the Integral. Dover, New York, 1964; Second edition. G. E. Stechert, New York, 1937.
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Bongiorno, D. Riemann-Type Definition of the Improper Integrals. Czechoslovak Mathematical Journal 54, 717–725 (2004). https://doi.org/10.1007/s10587-004-6420-x
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DOI: https://doi.org/10.1007/s10587-004-6420-x