Adjoint classes of functions in the $H\sb 1$ sense
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 2, pp. 505-522 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 26A39
Keywords: Stieltjes integral; Kurzweil integral; Henstock integral; ${\mathrm H}_1$-integral; Riemann-Lebesgue theorem; variational measure; adjoint classes
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Sworowski, Piotr. Adjoint classes of functions in the $H\sb 1$ sense. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 2, pp. 505-522. http://geodesic.mathdoc.fr/item/CMJ_2007_57_2_a0/

[1] H. Chen: A pair of adjoint classes of Riemann-Stieltjes integrable functions. Real Anal. Exch. 23 (1998), 235–240. | MR

[2] H. Chen: Adjoint classes of generalized Stieltjes integrable functions. Real Anal. Exch. 24 (1999), 139–148. | MR

[3] H. Chen: Adjoint classes of Lebesgue-Stieltjes integrable functions. Real Anal. Exch. 26 (2001), 421–427. | MR | Zbl

[4] I. J. L. Garces, P. Y. Lee: Cauchy and Harnack extensions for the $H_1$-integral. Matimyás Mat. 21 (1998), 28–34. | MR

[5] I. J. L. Garces, P. Y. Lee: Convergence theorems for the $H_1$-integral. Taiwanese J.  Math. 4 (2000), 439–445. | DOI | MR

[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

[7] A. Maliszewski, P. Sworowski: Uniform convergence theorem for the $H_1$-integral revisited. Taiwanese J.  Math. 7 (2003), 503–505. | DOI | MR

[8] A. Maliszewski, P. Sworowski: A characterization of $H_1$-integrable functions. Real Anal. Exch. 28 (2003), 93–104. | DOI | MR

[9] K. A. Ross: Another approach to Riemann-Stieltjes integrals. Am. Math. Mon. 87 (1980), 660–662. | DOI | MR | Zbl

[10] S. Saks: Theory of the Integral. G. E. Stechert, New York, 1937. | Zbl

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

[12] P. Sworowski: On $H_1$-integrable functions. Real Anal. Exch. 27 (2002), 275–286. | MR | Zbl

[13] P. Sworowski: Some comments on the $H_1$-integral. Real Anal. Exch. 29 (2004), 789–797. | MR | Zbl

[14] P. Sworowski: Adjoint classes for generalized Riemann-Stieltjes integrals. 27th Summer Symposium Conference Reports, Opava  2003. Real Anal. Exch. (2003), 41–45.

[15] B. S. Thomson: Real Functions. Lecture Notes in Mathematics, Vol. 1170. Springer-Verlag, Berlin, 1985. | MR