
theorem Th49:
for n be non zero Nat, f be PartFunc of CarProduct(Seg n --> REAL),ExtREAL,
  g be PartFunc of REAL n,ExtREAL,
  A be Element of Prod_Field(L-Field n), B be Element of XL-Field n
 st g = f*(CarProd(Seg n --> REAL))" & B = (CarProd(Seg n --> REAL)).:A
 holds f is A -measurable iff g is B -measurable
proof
    let n be non zero Nat,
    f be PartFunc of CarProduct(Seg n --> REAL),ExtREAL,
    g be PartFunc of REAL n ,ExtREAL,
    A be Element of Prod_Field(L-Field n), B be Element of XL-Field n;
    assume that
A1: g = f*(CarProd(Seg n --> REAL))" and
A2: B = (CarProd(Seg n --> REAL)).:A;
    product(Seg n --> REAL) = REAL n by SRINGS_5:8;
    hence thesis by A1,A2,Th34;
end;
