theorem Th52: :: LPSPACE2:52

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 k being positive Real
for x being Point of (Pre-Lp-Space (M,k)) st f in x & g in x holds
( f a.e.= g,M & Integral (M,((abs f) to_power k)) = Integral (M,((abs g) to_power k)) )