theorem Th36: :: MESFUN17:36

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