(a) If 9 : H --+ R is integrable and nonnegative on H, prove that there is an Xo E H such that I(Xo) L g(x) d:i; = L I(x)g(x) d:i;.

(b) If HO t- 0, prove that there is an open set V and a point Xo E V n H such that L I(x) d:i; = l(xo)Vol (H).