Previous |  Up |  Next

Article

Keywords:
Kurzweil-Henstock integral; Perron integral
Summary:
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.
References:
[1] Henstock R.: Lectures on the Theory of Integration. World Scientific Singapore (1988). MR 0963249 | Zbl 0668.28001
[2] Henstock R.: The General Theory of Integration. Clarendon Press Oxford (1991). MR 1134656 | Zbl 0745.26006
[3] Kurzweil J.: Nichtabsolut konvergente Integrale. BSB B.G. Teubner Verlagsgesellschaft Leipzig (1980). MR 0597703 | Zbl 0441.28001
[4] Lee Peng-Yee: Lanzhou Lectures on Henstock Integration. World Scientific Singapore (1989). MR 1050957 | Zbl 0699.26004
[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 0588510 | Zbl 0486.26005
[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 0017.30004
[9] Sklyarenko V.A.: On integration by parts for Burkill's SCP-integral. Mat. Sbornik 630-646 (1980), 112. MR 0587041
[10] Thomson B.S.: Derivation bases on the real line (II). Real Analysis Exchange 8 278-442 (1982-83). MR 0700194 | Zbl 0525.26003
Partner of
EuDML logo