ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 26A42, 26A39, 54A20 Jarník, Jiří, Fac. Educ. Charles Univ., Kurzweil, Jaroslav, Math. Inst. Acad. Sci., Czech Republic Convergence theorem for Henstock - Kurzweil integral based on the convergence of primitives We introduce certain compact subsets Q of the space ℂ of continuous functions, the elements of Q being primitives of functions integrable in the sense of Henstock-Kurzweil. The sets Q are described by a condition analogous to the Saks-Henstock lemma (up to sets of zero measure) and a condition of “variation zero”. Main result: If F is the limit in ℂ of F_{j} ∈ Q, j = 1, 2, …, then F ∈ Q and, moreover, f_{j} converge in measure to f provided F_{j}, F are the primitives of f_{j}, f. The relation of the convergence to (locally convex) topologies is studied. Reference: J. Kurzweil and J. Jarník, A convergence theorem for Henstock-Kurzweil integral and its relation to topology, Bull. Acad. Royale de Belgique, Cl. de Sciences, to appear