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Keywords:
integral; Kurzweil-Henstock integral; step-function; filterbase
Summary:
A short approach to the Kurzweil-Henstock integral is outlined, based on approximating a real function on a compact interval by suitable step-functions, and using filterbase convergence to define the integral. The properties of the integral are then easy to establish.
References:
[1] B. D. Craven: Lebesgue Measure and Integral. Pitman, Boston, 1982. MR 0733102 | Zbl 0491.28001
[2] J. Dugundji: Topology. Allyn & Bacon, Boston, 1966. MR 0193606 | Zbl 0144.21501
[3] R. Henstock: Linear Analysis. Butterworths, 1967. MR 0419707 | Zbl 0172.39001
[4] R. Henstock: The General Theory of Integration. Clarendon Press, Oxford, U.K., 1991. MR 1134656 | Zbl 0745.26006
[5] J. Kurzweil: Nichtabsolut konvergente Intgegrale. Teubner, Leipzig, 1980. MR 0597703
[6] S. Leader: The Kurzweil-Henstock Integral and its Differentials. Marcel Dekker, New York, 2001. MR 1837270 | Zbl 0984.26002
[7] Lee Peng-Yee: Lanzhou Lectures on Integration. World Scientific, Singapore, 1989. MR 1050957
[8] Lee Peng-Yee, R. Výborný: The Integral: an easy approach after Kurzweil and Henstock. Cambridge University Press, 2000. MR 1756319
[9] E. Schechter: Handbook of Analysis and its Foundations. Academic Press, San Diego, 1997 (Chapter 24: Generalized Riemann integrals). MR 1417259
[10] Š. Schwabik: Integration on $\mathbb{R}$: Kurzweil Theory. Charles University, Praha, 1999. (Czech)
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