Families of functions with equiabsolutely continuous integrals

The approximation of functions from Hardy classes by bounded analytic functions is investigated. A theorem is proved, characterizing the sets of functions with equiabsolutely continuous integrals as limit points of the family of bounded subsets of the space H.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 2, pp. 178–184, February, 1992.