
theorem Th79:
for X1,X2 be non empty set, S1 be SigmaField of X1, S2 be SigmaField of X2,
  M1 be sigma_Measure of S1,
  E be Element of sigma measurable_rectangles(S1,S2)
st
  E in Field_generated_by measurable_rectangles(S1,S2) holds
  (for B be Element of S1 holds
     E in {E where E is Element of sigma measurable_rectangles(S1,S2) :
          (ex F be Function of X2,ExtREAL st
            (for x be Element of X2 holds
               F.x = M1.(Measurable-Y-section(E,x) /\ B))
          & (for V be Element of S2 holds F is V-measurable))} )
proof
   let X1,X2 be non empty set, S1 be SigmaField of X1, S2 be SigmaField of X2,
   M1 be sigma_Measure of S1,
   E be Element of sigma measurable_rectangles(S1,S2);
   assume A0: E in Field_generated_by measurable_rectangles(S1,S2);
   let B be Element of S1;
    (ex F be Function of X2,ExtREAL st
      (for x be Element of X2 holds F.x = M1.(Measurable-Y-section(E,x) /\ B))
    & (for V be Element of S2 holds F is V-measurable)) by A0,Th77;
   hence thesis;
end;
