Henstock integration in the plane. (English) Zbl 0596.26005

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


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