theorem Th26: :: MESFUNC8:26

for X being non empty set
for S being SigmaField of X
for f being with_the_same_dom Functional_Sequence of X,ExtREAL
for g being PartFunc of X,ExtREAL
for E being Element of S st dom (f . 0) = E & ( for n being Nat holds f . n is_measurable_on E ) & dom g = E & ( for x being Element of X st x in E holds
( f # x is convergent & g . x = lim (f # x) ) ) holds
g is_measurable_on E