1. The problem statement, all variables and given/known data Let f:R^n-->R^n be a C^oo proper map. Suppose there is a real number r such that f(x)=x for all x in R^n with |x|> r. Show that for every compactly supported smooth n-form w on R^n integral of f*w = integral of w. Here, integral is defined on R^n. 2. Relevant equations I think this problem implies that when the condition above holds, we cannot construct a map from R to R s.t integral of w =/= integral of f*w which is not obvious for me. Could anybody provide a solution of the problem? 3. The attempt at a solution I don't even believe this result.