ON A PROBLEM OF MONGE

摘要

In 1942, I considered a general problem on the most profitable translocation of masses in a compact metric space. The problem is as follows: Assume that we are given two mass distributions determined by additive set functions Φ(e) and Φ'(e) with Φ(R) = Φ'(R) = 1. A translocation of masses is a function Ψ(e, e') that determines the mass translocated from a set e to a set e' with [Ψ(e, R) = Φ(e); Ψ(R, e) = Φ'(e)].