* 8. A sequence of functions f N : R --+ R is said to converge almost everywhere to a function f if and only if there is a set E of measure zero such that fN(X) --+ f(x), as N --+ 00, for every x E R \ E. Suppose that f is periodic on R. Prove that if f is Riemann integrable on [-n, n], then Ij N f --+ f almost everywhere as N --+ 00.