Authors: Suceavă, Bogdan D., California State University at Fullerton, Fullerton, CA 92834-6850 (bsuceava@fullerton.edu).
Distances generated by Barbilian's metrization procedure by oscillation of sublogarithmic functions, pp. 147-159.
ABSTRACT. Introduced originally in 1934, Barbilian’s metrization procedure induced a distance on a planar domain by a metric formula given by the so-called logarithmic oscillation. In 1959, Barbilian generalized this process to domains of a more general form, withstanding not necessarily on planar sets, but in a more abstract setting. In the present work, we show that there exists more general classes of distances than the ones produced by logarithmic oscillation. As a consequence, in Theorem 2 we state the most general form of Barbilian’s metrization procedure.