A class of distribution function processes which have derivatives

In the .author and van Eeden considered, as prior distributions for the cumulative, F, of the bio-assay problem, processes whose sample functions are, with probability one, distribution functions. The example we considered there had the undesirable property that its mean, E ( F ), was singular with respect to Lebesgue measure. In fact, Dubins and Freedman have shown that a class of such processes, which includes the example we considered, has sample functions F which are, with probability one, singular.