Generalized multidimensional Perron integral involving a new regularity condition. (English) Zbl 0782.26003

The Riemannian definitions of generalized multidimensional Perron integral introduced in the last twelve years make use of various types of regularity concepts for the partial intervals involved in the Riemann sums. The aim of this paper is to generalize the definition of the \(\alpha\)-regular integral introduced earlier by the same authors by replacing the constant \(\alpha\) by some function \(\rho\), and to study the dependence of the integrals with respect to \(\rho\). En passant, the authors answer a question posed by Pfeffer at the 15th Summer Symposium in Real Analysis at Smolenice in 1991.


26B15 Integration of real functions of several variables: length, area, volume
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