Let S be a closed n-cube with v(S) > 0. Suppose f : S –→ R is continuous on S 0 for all closed n-cube R C S with v(R) > 0. Prove that f(x) = 0 for all £4 and that SR f x E S. (Suppose towards a contradiction that |f(xo)| > 0 for some xo E S. First prove that there exists a closed n-cube P C S containing xo such that v(P) > 0 and |f(x)| > |f(xo)| for all x E P.)