theorem Th21: :: MESFUNC8:21

for X being non empty set
for S being SigmaField of X
for f being Functional_Sequence of X,ExtREAL
for F being SetSequence of S
for r being Real st ( for n being Nat holds F . n = (dom (f . 0)) /\ (great_eq_dom (((superior_realsequence f) . n),r)) ) holds
meet F = (dom (f . 0)) /\ (great_eq_dom ((lim_sup f),r))