Abstract:
Several properties of generalized multivariate integrals are considered.
In the two-dimensional case the consistency of the regular Perron integral
is proved, as well as the consistency of a generalized integral solving the problem of the recovery of the coefficients of double Haar series in a certain
class. Several generalizations of Skvortsov's well-known theorem are
obtained as consequences, for instance, the following result: if
a double Haar series converges for some
$\rho\in(0,1/2]$$\rho$-regularly everywhere in the
unit square to a finite function that is Perron-integrable in the
$\rho$-regular sense, then the series in question is the
Fourier–Perron series of its sum.
Bibliography: 20 titles.