Suppose that Ï{B) and ɸ(E) are Cp surfaces and that Ï = ɸ o Ï, where Ï

Suppose that ψ{B) and ɸ(E) are Cp surfaces and that ψ = ɸ o τ, where τ is a C1 function from B onto Z.
a) If (f, B) and (0, E) are smooth and Ï„ is 1-1 with Δτ ‰  0 on B, prove that

for all continuous g : ɸ(E) †’ R.
b) If Z is a closed subset of B of area zero such that (ψ, B) is smooth off Z, Ï„ is 1-1, and Δτ ‰  0 on B°Z, prove that

for all continuous g : ɸ(E) †’ R.

Transcribed Image Text:

||E g@cu. u))|| NOu, uil du du / g(ψ(s, t)) ll Νψ (s til ds dt