theorem Th100: :: MESFUNC5:100

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,ExtREAL st ex A being Element of S st
( A = dom f & f is A -measurable ) holds
( f is_integrable_on M iff |.f.| is_integrable_on M )