theorem Th52: :: MESFUN16:52

for I, 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
for G2 being PartFunc of REAL,REAL st [:I,J:] = dom f & f is_continuous_on [:I,J:] & f = g & G2 = (Integral2 (L-Meas,|.(R_EAL g).|)) | I holds
G2 is continuous