zbMATH — the first resource for mathematics

Equivalence of two definitions of a double regular integral on the plane. (English. Russian original) Zbl 0988.26012
Mosc. Univ. Math. Bull. 55, No. 5, 28-31 (2000); translation from Vestn. Mosk. Univ., Ser. I 2000, No. 5, 50-53 (2000).
In the paper the equivalence of two types of definitions of the double regular integral on the plane is discussed, namely, the Henstock definition in which the generalized Riemann sums are used and the descriptive definition in terms of primitives. The author presents a direct proof of the equivalence of the constructive and descriptive double regular integral in \(\mathbb{R}^2\). In [R. A. Gordon, Real. Anal. Exch. 16, No. 1, 154-168 (1991; Zbl 0723.26005)] similar problems are considered for the one-dimensional case.
26B99 Functions of several variables
26A39 Denjoy and Perron integrals, other special integrals