5. Suppose that 'ljJ(B) and ¢(E) are CP surfaces, and 'ljJ = ¢ 0 T, where T is a C1 function from B onto Z.

(a) If ('ljJ, B) and (¢, E) are smooth and T is 1-1 with ~r =I- 0 on B, prove that f Is g(¢(u,v))IIN(u,v)11 dudv = fL g('ljJ(s, t))IIN",(s, t)11 dsdt for all continuous 9 : ¢(E) -+ R.

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(b) If Z is a closed subset of B of area zero such that ('ljJ, B) is smooth off Z, T is 1-1, and ~r =I- 0 on BO \ Z, prove that f Is g(¢(u, v))IIN(u,v)11 dudv = f L g('ljJ(s, t))IIN",(s, t)11 dsdt for all continuous 9 : ¢(E) -+ R.