Random set theory is a useful tool to quantify lower and upper bounds on the probability of
the occurrence of events given uncertain information represented for example by possibility
distributions, probability boxes, or Dempster–Shafer structures, among others. In this paper it
is shown that the belief and plausibility estimated by Dempster–Shafer evidence theory are
basically approximations by Riemann–Stieltjes sums of the integrals of the lower and upper
probability employed when using infinite random sets of indexable type. In addition, it is …