theorem Th22: :: MESFUNC8:22

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_dom (((inferior_realsequence f) . n),r)) ) holds
union (rng F) = (dom (f . 0)) /\ (great_dom ((lim_inf f),r))