On Kurzweil-Stieltjes equiintegrability and generalized BV functions
Mathematica Bohemica, Tome 144 (2019) no. 4, pp. 423-436
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We present sufficient conditions ensuring Kurzweil-Stieltjes equiintegrability in the case when integrators belong to the class of functions of generalized bounded variation.
We present sufficient conditions ensuring Kurzweil-Stieltjes equiintegrability in the case when integrators belong to the class of functions of generalized bounded variation.
DOI : 10.21136/MB.2019.0041-19
Classification : 26A24, 26A39, 26A42, 26A45
Keywords: Kurzweil-Stieltjes integral; generalized bounded variation; variational measure; Stieltjes derivative
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Monteiro, Giselle A. On Kurzweil-Stieltjes equiintegrability and generalized BV functions. Mathematica Bohemica, Tome 144 (2019) no. 4, pp. 423-436. doi: 10.21136/MB.2019.0041-19

[1] Bongiorno, B., Piazza, L. Di: Convergence theorems for generalized Riemann-Stieltjes integrals. Real Anal. Exch. 17 (1991-92), 339-361. | DOI | MR | JFM

[2] Bongiorno, B., Piazza, L. Di, Skvortsov, V.: A new full descriptive characterization of \hbox{Denjoy-Perron} integral. Real Anal. Exch. 21 (1995-96), 656-663. | DOI | MR | JFM

[3] Faure, C.-A.: A descriptive definition of the KH-Stieltjes integral. Real Anal. Exch. 23 (1998-99), 113-124. | DOI | MR | JFM

[4] Fraňková, D.: Regulated functions. Math. Bohem. 116 (1991), 20-59. | MR | JFM

[5] Frigon, M., Pouso, R. L.: Theory and applications of first-order systems of Stieltjes differential equations. Adv. Nonlinear Anal. 6 (2017), 13-36. | DOI | MR | JFM

[6] Gordon, R. A.: Another look at a convergence theorem for the Henstock integral. Real Anal. Exch. 15 (1989-90), 724-728. | DOI | MR | JFM

[7] Gordon, R. A.: The Integrals of Lebesgue, Denjoy, Perron, and Henstock. Graduate Studies in Mathematics 4. AMS, Providence (1994). | DOI | MR | JFM

[8] Hoffmann, H.: Descriptive Characterisation of the Variational Henstock-Kurzweil-Stieltjes Integral and Applications. PhD thesis. Karlsruher Institue of Technology, Karlsruhe. Available at https://publikationen.bibliothek.kit.edu/1000046600 (2014).

[9] Kurzweil, J., Jarník, J.: Equiintegrability and controlled convergence of Perron-type integrable functions. Real Anal. Exch. 17 (1991-92), 110-139. | DOI | MR | JFM

[10] Lee, P. Y.: Lanzhou Lectures on Henstock Integration. Series in Real Analysis 2. World Scientific, London (1989). | DOI | MR | JFM

[11] Monteiro, G. A., Satco, B.: Distributional, differential and integral problems: equivalence and existence results. Electron. J. Qual. Theory Differ. Equ. 2017 (2017), Paper No. 7, 26 pages. | DOI | MR | JFM

[12] Monteiro, G. A., Slavík, A., Tvrdý, M.: Kurzweil-Stieltjes Integral. Theory and Applications. Series in Real Analysis 15. World Scientific, Hackensack (2019). | DOI | MR | JFM

[13] Pouso, R. L., Rodríguez, A.: A new unification of continuous, discrete, and impulsive calculus through Stieltjes derivatives. Real Anal. Exch. 40 (2015), 319-354. | DOI | MR | JFM

[14] Saks, S.: Theory of the Integral. With two additional notes by Stefan Banach. Monografie Matematyczne Tom. 7. G. E. Stechert & Co., New York (1937). | MR | JFM

[15] Satco, B.-R.: Measure integral inclusions with fast oscillating data. Electron. J. Differ. Equ. 2015 (2015), Paper No. 107, 13 pages. | MR | JFM

[16] Schwabik, Š.: Variational measures and the Kurzweil-Henstock integral. Math. Slovaca 59 (2009), 731-752. | DOI | MR | JFM

[17] Schwabik, Š.: General integration and extensions I. Czech. Math. J. 60 (2010), 961-981. | DOI | MR | JFM

[18] Schwabik, Š.: General integration and extensions II. Czech. Math. J. 60 (2010), 983-1005. | DOI | MR | JFM

[19] Schwabik, Š., Vrkoč, I.: On Kurzweil-Henstock equiintegrable sequences. Math. Bohem. 121 (1996), 189-207. | DOI | MR | JFM

[20] Schwabik, Š., Ye, G.: Topics in Banach Space Integration. Series in Real Analysis 10. World Scientific, Hackensack (2005). | DOI | MR | JFM

[21] Thomson, B. S.: Real Functions. Lecture Notes in Mathematics 1170. Springer, Berlin (1985). | DOI | MR | JFM

[22] Ward, A. J.: The Perron-Stieltjes integral. Math. Z. 41 (1936), 578-604. | DOI | MR | JFM

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