theorem Th34: :: MESFUN18:34

for n being non zero Nat
for I being Subset of (CarProduct ((Seg n) --> REAL))
for J being closed_interval Subset of REAL
for f being PartFunc of [:(CarProduct ((Seg n) --> RNS_Real)),RNS_Real:],RNS_Real
for g being PartFunc of [:(CarProduct ((Seg n) --> REAL)),REAL:],REAL st [:I,J:] = dom f & f is_continuous_on [:I,J:] & f = g holds
( Integral2 (L-Meas,|.(R_EAL g).|) is PartFunc of (CarProduct ((Seg n) --> REAL)),REAL & Integral2 (L-Meas,(R_EAL g)) is PartFunc of (CarProduct ((Seg n) --> REAL)),REAL )