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Title: Adjoint classes of functions in the $H\sb 1$ sense (English)
Author: Sworowski, Piotr
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 57
Issue: 2
Year: 2007
Pages: 505-522
Summary lang: English
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Category: math
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Summary: Using the concept of the $ {\mathrm H}_1$-integral, we consider a similarly defined Stieltjes integral. We prove a Riemann-Lebesgue type theorem for this integral and give examples of adjoint classes of functions. (English)
Keyword: Stieltjes integral
Keyword: Kurzweil integral
Keyword: Henstock integral
Keyword: ${\mathrm H}_1$-integral
Keyword: Riemann-Lebesgue theorem
Keyword: variational measure
Keyword: adjoint classes
MSC: 26A39
idZBL: Zbl 1174.26310
idMR: MR2337612
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Date available: 2009-09-24T11:47:20Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/128187
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Reference: [1] H. Chen: A pair of adjoint classes of Riemann-Stieltjes integrable functions.Real Anal. Exch. 23 (1998), 235–240. MR 1609806
Reference: [2] H. Chen: Adjoint classes of generalized Stieltjes integrable functions.Real Anal. Exch. 24 (1999), 139–148. MR 1691741
Reference: [3] H. Chen: Adjoint classes of Lebesgue-Stieltjes integrable functions.Real Anal. Exch. 26 (2001), 421–427. Zbl 1023.26007, MR 1825521
Reference: [4] I. J. L. Garces, P. Y. Lee: Cauchy and Harnack extensions for the $H_1$-integral.Matimyás Mat. 21 (1998), 28–34. MR 1710941
Reference: [5] I. J. L. Garces, P. Y. Lee: Convergence theorems for the $H_1$-integral.Taiwanese J.  Math. 4 (2000), 439–445. MR 1779108, 10.11650/twjm/1500407260
Reference: [6] I. J. L. Garces, P. Y. Lee, and D. Zhao: Moore-Smith limits and the Henstock integral.Real Anal. Exch. 24 (1999), 447–455. MR 1691764
Reference: [7] A. Maliszewski, P. Sworowski: Uniform convergence theorem for the $H_1$-integral revisited.Taiwanese J.  Math. 7 (2003), 503–505. MR 1998771, 10.11650/twjm/1500558401
Reference: [8] A. Maliszewski, P. Sworowski: A characterization of $H_1$-integrable functions.Real Anal. Exch. 28 (2003), 93–104. MR 1973971, 10.14321/realanalexch.28.1.0093
Reference: [9] K. A. Ross: Another approach to Riemann-Stieltjes integrals.Am. Math. Mon. 87 (1980), 660–662. Zbl 0446.26005, MR 0600928, 10.2307/2320958
Reference: [10] S. Saks: Theory of the Integral.G. E. Stechert, New York, 1937. Zbl 0017.30004
Reference: [11] Š. Schwabik: On the relation between Young’s and Kurzweil’s concept of Stieltjes integral.Cas. Pest. Mat. 98 (1973), 237–251. Zbl 0266.26006, MR 0322113
Reference: [12] P. Sworowski: On $H_1$-integrable functions.Real Anal. Exch. 27 (2002), 275–286. Zbl 1015.26017, MR 1887858
Reference: [13] P. Sworowski: Some comments on the $H_1$-integral.Real Anal. Exch. 29 (2004), 789–797. Zbl 1078.26008, MR 2083813
Reference: [14] P. Sworowski: Adjoint classes for generalized Riemann-Stieltjes integrals. 27th Summer Symposium Conference Reports, Opava  2003.Real Anal. Exch. (2003), 41–45.
Reference: [15] B. S. Thomson: Real Functions. Lecture Notes in Mathematics, Vol. 1170.Springer-Verlag, Berlin, 1985. MR 0818744
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