theorem Th43: :: MESFUN18:43

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