theorem Th48: :: LPSPACE1:48

for X being non empty set
for S being SigmaField of X
for M being sigma_Measure of S
for f, g being PartFunc of X,REAL
for x being Point of (Pre-L-Space M) st f in x & g in x holds
( f a.e.= g,M & Integral (M,f) = Integral (M,g) & Integral (M,(abs f)) = Integral (M,(abs g)) )