theorem Th55: :: LPSPACE2:55

for X being non empty set
for S being SigmaField of X
for M being sigma_Measure of S
for f being PartFunc of X,REAL
for k being positive Real
for x being Point of (Lp-Space (M,k)) st f in x holds
( x = a.e-eq-class_Lp (f,M,k) & ex r being Real st
( 0 <= r & r = Integral (M,((abs f) to_power k)) & ||.x.|| = r to_power (1 / k) ) )