theorem Th56: :: MESFUN16:56

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 G1 being PartFunc of REAL,REAL st [:I,J:] = dom f & f is_continuous_on [:I,J:] & f = g & G1 = (Integral1 (L-Meas,(R_EAL g))) | J holds
G1 is continuous