A note on the cake-division problem (Q1075937)

Let C (the cake) be a compact convex set, and let each of n people define a non-atomic probability measure on the Borel sets of C. It is well known that C can be divided among the n people so that each receives at least 1/n of it (in his own measure), and even, if the n measures are not all identical, so that each receives more than 1/n of it. No constructive proof was known of this latter result. This note provides one.