
theorem :: Fubini's theorem
for X1,X2 be non empty set, S1 be SigmaField of X1, S2 be SigmaField of X2,
 M1 be sigma_Measure of S1, M2 be sigma_Measure of S2,
 A be Element of sigma measurable_rectangles(S1,S2),
 f be PartFunc of [:X1,X2:],ExtREAL
st M1 is sigma_finite & M2 is sigma_finite
 & (f is nonnegative or f is nonpositive) & A = dom f & f is A-measurable
 holds Integral(Prod_Measure(M1,M2),f) = Integral(M2,Integral1(M1,f))
     & Integral(Prod_Measure(M1,M2),f) = Integral(M1,Integral2(M2,f))
by Lm16,Lm18,Lm17,Lm19;
