theorem :: MESFUN7C:42

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,COMPLEX st f is_integrable_on M & g is_integrable_on M holds
ex E being Element of S st
( E = dom (f + g) & Integral (M,(|.(f + g).| | E)) <= (Integral (M,(|.f.| | E))) + (Integral (M,(|.g.| | E))) )