theorem Th42: :: MESFUN17:42

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 E being Element of sigma (measurable_rectangles (L-Field,L-Field)) st [:[:I,J:],K:] = dom f & f is_continuous_on [:[:I,J:],K:] & f = g holds
Integral2 (L-Meas,|.(R_EAL g).|) is E -measurable