theorem :: LPSPACE2:46

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 a being Real
for k being positive Real st ex E being Element of S st
( M . (E `) = 0 & dom f = E & f is E -measurable ) & ex E being Element of S st
( M . (E `) = 0 & dom g = E & g is E -measurable ) & not a.e-eq-class_Lp (f,M,k) is empty & a.e-eq-class_Lp (f,M,k) = a.e-eq-class_Lp (g,M,k) holds
a.e-eq-class_Lp ((a (#) f),M,k) = a.e-eq-class_Lp ((a (#) g),M,k)