Problem 9.4. Let G and G1 be bounded open subsets of R" such that G1 CG. Construct a function h E C O such that h = 1 in G1 and h = ( outside G. (Hint: Choose an open set G2 such that G1 C G2, G2 C G. Let h = XG, * K for a KE C with suitably small support and S K = 1.) Problem 9.4. Let G and G1 be bounded open subsets of R" such that G1 CG. Construct a function h E C O such that h = 1 in G1 and h = ( outside G. (Hint: Choose an open set G2 such that G1 C G2, G2 C G. Let h = XG, * K for a KE C with suitably small support and S K = 1.)