Compactness in the quasi-absolutely continuous functions space

In this paper we introduce the notion of a quasi-continuous function on a closed segment and obtain the set compactness condition in the functions quasi-absolutely continuous space on a closed segment. The class completeness allows us to replace a continuous function by a approximations sequence, each of which is "simpler" than the original one. The differential equations investigating solutions simplifying process problem is solved, for which a constructing an absolutely continuous function method is proposed.