theorem Th35: :: MESFUN7C:35

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 st f is_integrable_on M holds
( ex A being Element of S st
( A = dom f & f is_measurable_on A ) & |.f.| is_integrable_on M )