theorem Th12: :: MESFUNC8:12

for X being non empty set
for f being Functional_Sequence of X,ExtREAL holds
( ( for x being Element of X st x in dom (lim_sup f) holds
( (lim_sup f) . x = inf (superior_realsequence (f # x)) & (lim_sup f) . x = inf ((superior_realsequence f) # x) & (lim_sup f) . x = (inf (superior_realsequence f)) . x ) ) & lim_sup f = inf (superior_realsequence f) )