Semin. Teor. Probab. Apl. 80, 8 p. (1986).
An alternative version of the triangle inequality for a subclass of probabilistic semi-metric spaces is proposed and studied. Let the function f: [0,1] be continuous and strictly decreasing with . The probabilistic semi-metric space (S, is called a probabilistic f-metric structure provided the mapping (where is denoted Fpq) satisfies the following triangle inequality: Given there is a such that , whenever
It is shown that every Menger (-Menger) space (S, in which is also a probabilistic f-metric structure for any f and that all such probabilistic f-metric structures generate a uniformity for S which is equivalent to the - uniformity. Two recipes for constructing a metric for the - uniformity are given which use the function f.