
theorem Th50:
for f1 be PartFunc of [:REAL,REAL:],ExtREAL,
    f2 be PartFunc of CarProduct(Seg 2 --> REAL),ExtREAL,
    A1 be Element of sigma measurable_rectangles(L-Field,L-Field),
    A2 be Element of Prod_Field(L-Field 2) st f1 = f2 & A1 = A2 holds
  f1 is A1-measurable iff f2 is A2-measurable
proof
    let f1 be PartFunc of [:REAL,REAL:],ExtREAL,
    f2 be PartFunc of CarProduct(Seg 2 --> REAL),ExtREAL,
    A1 be Element of sigma measurable_rectangles(L-Field,L-Field),
    A2 be Element of Prod_Field(L-Field 2);
    assume that
A1: f1 = f2 and
A2: A1 = A2;

    Prod_Field(L-Field (1+1))
     = sigma measurable_rectangles(Prod_Field(L-Field 1),L-Field) by Th44;
    hence thesis by A1,A2,Th37,Th41;
end;
