theorem Th32: :: MESFUN17:32

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