theorem Th23: :: MESFUN14:23

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
for E being Element of S
for n being Nat st E = dom f & f is nonnegative & f is E -measurable & Integral (M,f) = 0 holds
M . (E /\ (great_eq_dom (f,(1 / (n + 1))))) = 0