The Kurzweil integral with exclusion of negligible sets
Mathematica Bohemica, Tome 128 (2003) no. 3, pp. 277-292

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MR Zbl
We propose an extended version of the Kurzweil integral which contains both the Young and the Kurzweil integral as special cases. The construction is based on a reduction of the class of $\delta $-fine partitions by excluding small sets.
We propose an extended version of the Kurzweil integral which contains both the Young and the Kurzweil integral as special cases. The construction is based on a reduction of the class of $\delta $-fine partitions by excluding small sets.
DOI : 10.21136/MB.2003.134183
Classification : 26A39, 26A42
Keywords: Kurzweil integral; Young integral
Krejčí, Pavel. The Kurzweil integral with exclusion of negligible sets. Mathematica Bohemica, Tome 128 (2003) no. 3, pp. 277-292. doi: 10.21136/MB.2003.134183
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[1] G. Aumann: Reelle Funktionen. Springer, Berlin, 1954. (German) | MR | Zbl

[2] M. Brokate, P. Krejčí: Duality in the space of regulated functions and the play operator. Math. Z. (Accepted). | MR

[3] T. H. Hildebrandt: Introduction to the Theory of Integration. Academic Press, New York and London, 1963. | MR | Zbl

[4] P. Krejčí, J. Kurzweil: A nonexistence result for the Kurzweil integral. Math. Bohem. 127 (2002), 571–580. | MR

[5] P. Krejčí, Ph. Laurençot: Generalized variational inequalities. J. Convex Anal. 9 (2002), 159–183. | MR

[6] J. Kurzweil: Generalized ordinary differential equations and continuous dependence on a parameter. Czechoslovak Math. J. 7 (1957), 418–449. | MR | Zbl

[7] Š. Schwabik: On the relation between Young’s and Kurzweil’s concept of Stieltjes integral. Čas. Pěst. Mat. 98 (1973), 237–251. | MR | Zbl

[8] Š. Schwabik: On a modified sum integral of Stieltjes type. Čas. Pěst. Mat. 98 (1973), 274–277. | MR | Zbl

[9] Š. Schwabik: Abstract Perron-Stieltjes integral. Math. Bohem. 121 (1996), 425–447. | MR | Zbl

[10] M. Tvrdý: Regulated functions and the Perron-Stieltjes integral. Čas. Pěst. Mat. 114 (1989), 187–209. | MR

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