theorem :: MESFUN17:52

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 y being Element of REAL st [:[:I,J:],K:] = dom f & f is_continuous_on [:[:I,J:],K:] & f = g holds
( ProjPMap2 ((Integral2 (L-Meas,(R_EAL g))),y) is Function of REAL,REAL & ProjPMap2 (|.(Integral2 (L-Meas,(R_EAL g))).|,y) is Function of REAL,REAL )