theorem Th51: :: LPSPACE1:51

for a being Real
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, y being Point of (L-1-Space M) holds
( ( f in x & g in y implies f + g in x + y ) & ( f in x implies a (#) f in a * x ) )