theorem Th57: :: MESFUN12:57

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 dom f in S & ( for x being Element of X st x in dom f holds
0 = f . x ) holds
( ( for E being Element of S st E c= dom f holds
f is E -measurable ) & Integral (M,f) = 0 )