theorem Th51: :: MESFUN16:51

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