
theorem
for n be non zero Nat, f be PartFunc of CarProduct(Seg n --> REAL),ExtREAL,
  g be PartFunc of REAL n,ExtREAL
 st g = f*(CarProd(Seg n --> REAL))" holds
  f is_integrable_on Prod_Measure(L-Meas n) iff g is_integrable_on XL-Meas n
proof
    let n be non zero Nat,
    f be PartFunc of CarProduct(Seg n --> REAL),ExtREAL,
    g be PartFunc of REAL n,ExtREAL;
    assume
A1: g = f*(CarProd(Seg n --> REAL))";
    product(Seg n --> REAL) = REAL n by SRINGS_5:8;
    hence thesis by A1,Th36;
end;
