theorem :: MESFUN6C:21

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,COMPLEX
for A being Element of S st ex E being Element of S st
( E = dom f & f is E -measurable ) & M . A = 0 holds
( f | A is_integrable_on M & Integral (M,(f | A)) = 0 )