for X being non empty set
for S being SigmaField of X
for f being with_the_same_dom Functional_Sequence of X,COMPLEX
for g being PartFunc of X,COMPLEX
for E being Element of S st dom (f . 0) = E & ( for n being Nat holds f . n is E -measurable ) & 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 E -measurable