Henstock integration in the plane. (English) Zbl 0596.26005

Ostaszewski, Krzysztof M.

Mem. Am. Math. Soc. 353, 106 p. (1986).

This paper is devoted to a comparison of various integration theories in the plane by introducing corresponding derivation bases and a corresponding Henstock integral. In this way, the author obtains comparisons results for the nonabsolute integrals of Perron, Kempisty, the reviewer, Pfeffer and Chelidze-Dzhvarshejshvili. The paper also contains results on the Fubini theorem. Besides the new results it contains, this work constitutes an interesting comparative study of a number of ancient and recent nonabsolute integrals and a step toward the unification of their presentation.

Reviewer: J.Mawhin

MSC:

26A39	Denjoy and Perron integrals, other special integrals
26B15	Integration of real functions of several variables: length, area, volume

Keywords:

variational integral; Perron integral; Burkill integral; Kempisty; integral; comparison of various integration theories; derivation bases; Henstock integral; nonabsolute integrals; Fubini theorem