Exercise 5 (#6.7). Let fi, ..., fm+1 be Borel functions on RP that are in- tegrable with respect to a o-finite measure v. For given constants t, ..., tm, let T be the class of Borel functions o (from RP to [0, 1]) satisfying | 05;dv stil i= 1, ..., m, and to be the set of o's in T satisfying |vl,= t, i=1, ..., m. Show that if there are constants ci, ..., Cm such that 0=(x) = { 0 fm+1(x) >cf(2) + + Cm fm(2) fm+1(x) 0 for all i, then ou maximizes ofm+1dv over o E T