Geodesic
A step to Kurzweil-Henstock—an outline
Mathematica Bohemica, Tome 129 (2004) no. 3, pp. 297-304

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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.
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.
DOI : 10.21136/MB.2004.134150
Classification : 26A39
Keywords: integral; Kurzweil-Henstock integral; step-function; filterbase 
Craven, B. D. A step to Kurzweil-Henstock—an outline. Mathematica Bohemica, Tome 129 (2004) no. 3, pp. 297-304. doi: 10.21136/MB.2004.134150
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[2] J. Dugundji: Topology. Allyn & Bacon, Boston, 1966. | MR | Zbl

[3] R. Henstock: Linear Analysis. Butterworths, 1967. | MR | Zbl

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[6] S. Leader: The Kurzweil-Henstock Integral and its Differentials. Marcel Dekker, New York, 2001. | MR | Zbl

[7] Lee Peng-Yee: Lanzhou Lectures on Integration. World Scientific, Singapore, 1989. | MR

[8] Lee Peng-Yee, R. Výborný: The Integral: an easy approach after Kurzweil and Henstock. Cambridge University Press, 2000. | MR

[9] E. Schechter: Handbook of Analysis and its Foundations. Academic Press, San Diego, 1997 (Chapter 24: Generalized Riemann integrals). | MR

[10] Š. Schwabik: Integration on $\mathbb{R}$: Kurzweil Theory. Charles University, Praha, 1999. (Czech)

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