I don't get this problem.

If g is monotone increasing on J, and if f and f., ne N, are functions which are integrable with respect to g, then we say that the sequence (f.) converges in mean (with respect to g) in case life - fil - 0. (The notation here is the same as in the preceding exercise.) Show that if (f.) converges in mean to f, then Prove that if a sequence (f.) of integrable functions converges uniformly on J to f, then it also converges in mean to f. In fact, llf. - flhi s 18(b) - 8(a)} llfm -flls. However, if f. denotes the function in Example 31.1, and if g. = (1)f., then the sequence (gn) converges in mean [with respect to g (x) = x] to the zero function, but the convergence is not uniform on