Geodesic
Convergence theorems for the Perron integral and Sklyarenko's condition
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 2, pp. 237-244 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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It is shown that a uniform version of Sklyarenko's integrability condition for Perron integrals together with pointwise convergence of a sequence of integrable functions are sufficient for a convergence theorem for Perron integrals.
It is shown that a uniform version of Sklyarenko's integrability condition for Perron integrals together with pointwise convergence of a sequence of integrable functions are sufficient for a convergence theorem for Perron integrals.
Classification : 26A39
Keywords: Kurzweil-Henstock integral; Perron integral 
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     title = {Convergence theorems for the {Perron} integral and {Sklyarenko's} condition},
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Schwabik, Štefan. Convergence theorems for the Perron integral and Sklyarenko's condition. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 2, pp. 237-244. http://geodesic.mathdoc.fr/item/CMUC_1992_33_2_a3/

[1] Henstock R.: Lectures on the Theory of Integration. World Scientific Singapore (1988). | MR | Zbl

[2] Henstock R.: The General Theory of Integration. Clarendon Press Oxford (1991). | MR | Zbl

[3] Kurzweil J.: Nichtabsolut konvergente Integrale. BSB B.G. Teubner Verlagsgesellschaft Leipzig (1980). | MR | Zbl

[4] Lee Peng-Yee: Lanzhou Lectures on Henstock Integration. World Scientific Singapore (1989). | MR | Zbl

[5] Mawhin J.: Introduction à l'Analyse. CABAY, Libraire-éditeur Louvain-La-Neuve (1984).

[6] McLeod R.M.: The Generalized Riemann Integral. Math. Assoc. of America (1980). | MR | Zbl

[7] Preiss D., Schwabik Š.: The definite integral. Mimeographed notes in Czech Math.-Phys. Fac. of the Charles Univ. and Math. Inst. of the Czech. Acad. Sci Prague (1979), 138 pages.

[8] Saks S.: Theory of the integral. Warszawa (1937). | Zbl

[9] Sklyarenko V.A.: On integration by parts for Burkill's SCP-integral. Mat. Sbornik 630-646 (1980), 112. | MR

[10] Thomson B.S.: Derivation bases on the real line (II). Real Analysis Exchange 8 278-442 (1982-83). | MR | Zbl