theorem Th33: :: MESFUN18:33

for n being non zero Nat
for I being Subset of (CarProduct ((Seg n) --> REAL))
for J being Subset of REAL
for f being PartFunc of [:(CarProduct ((Seg n) --> RNS_Real)),RNS_Real:],RNS_Real
for g being PartFunc of [:(CarProduct ((Seg n) --> REAL)),REAL:],REAL
for E being Element of sigma (measurable_rectangles ((Prod_Field (L-Field n)),L-Field)) st [:I,J:] = dom f & f is_continuous_on [:I,J:] & f = g & E = [:I,J:] holds
g is E -measurable