
theorem
for X1,X2 be non empty set, S1 be SigmaField of X1, S2 be SigmaField of X2,
 M2 be sigma_Measure of S2,
 f be disjoint_valued FinSequence of measurable_rectangles(S1,S2),
 x be Element of X1, n be Nat,
 En be Element of sigma measurable_rectangles(S1,S2),
 An be Element of S1, Bn be Element of S2
 st n in dom f & f.n = En & En = [:An,Bn:] holds
  Integral(M2,ProjMap1(chi(f.n,[:X1,X2:]),x))
     = M2.(Measurable-X-section(En,x)) * chi(An,X1).x by Th65;
