theorem :: MESFUN17:51

for I, J, K being non empty closed_interval Subset of REAL
for f being PartFunc of [:[:RNS_Real,RNS_Real:],RNS_Real:],RNS_Real
for g being PartFunc of [:[:REAL,REAL:],REAL:],REAL
for x being Element of REAL st [:[:I,J:],K:] = dom f & f is_continuous_on [:[:I,J:],K:] & f = g holds
( ProjPMap1 ((Integral2 (L-Meas,(R_EAL g))),x) is Function of REAL,REAL & ProjPMap1 (|.(Integral2 (L-Meas,(R_EAL g))).|,x) is Function of REAL,REAL )