Remarks on Agronsky's theorem on strong containment and continuity roads (Q1065174)

In his paper in Real Anal. Exch. 9, 195-205 (1984; Zbl 0572.26002) \textit{S. J. Agronsky} gives some conditions under which a real function of one real variable, measurable relative to a family of sets, may be characterized as that possessing a continuity road of some properties at every point. The paper under review contains some improvements on Agronsky's theorem. It is shown that some of his assumptions are redundant, among them that saying that the function belongs to the Baire class one.