theorem :: MESFUN18:63

for n being non zero Nat
for D being b₁ -element FinSequence
for f being PartFunc of (REAL-NS n),RNS_Real
for g being PartFunc of (REAL n),REAL
for G being PartFunc of (CarProduct ((Seg n) --> REAL)),REAL st ( for i being Nat st i in Seg n holds
D . i is closed_interval Subset of REAL ) & f is_continuous_on product D & dom f = product D & g = f & G = f * (CarProd ((Seg n) --> REAL)) holds
( G is_integrable_on Prod_Measure (L-Meas n) & g is_integrable_on XL-Meas n & Integral ((XL-Meas n),g) = Integral ((Prod_Measure (L-Meas n)),G) )