theorem Th44: :: MESFUN14:44

for X being non empty set
for S being SigmaField of X
for M being sigma_Measure of S
for f, g being PartFunc of X,REAL
for E being Element of S st M is complete & f is_integrable_on M & f a.e.= g,M & E = dom f & E = dom g holds
( g is_integrable_on M & Integral (M,f) = Integral (M,g) )