
theorem Th36:
for n be non zero Nat, X be non-empty n-element FinSequence,
    S be sigmaFieldFamily of X, m be sigmaMeasureFamily of S,
    f be PartFunc of CarProduct X,ExtREAL,
    g be PartFunc of product X,ExtREAL st g = f*(CarProd X)" holds
    f is_integrable_on Prod_Measure m iff g is_integrable_on XProd_Measure m
proof
    let n be non zero Nat, X be non-empty n-element FinSequence,
    S be sigmaFieldFamily of X, m be sigmaMeasureFamily of S,
    f be PartFunc of CarProduct X,ExtREAL,
    g be PartFunc of product X,ExtREAL;
    assume
A1: g = f*(CarProd X)";
    CarProd X is bijective by Th12;
    hence thesis by Th33,A1;
end;
