theorem Th95: :: MEASUR11:96

for X1, X2 being non empty set
for S1 being SigmaField of X1
for S2 being SigmaField of X2
for M1 being sigma_Measure of S1
for M2 being sigma_Measure of S2
for E1, E2 being Element of sigma (measurable_rectangles (S1,S2)) st M1 is sigma_finite & E1 misses E2 holds
Integral (M2,(X-vol ((E1 \/ E2),M1))) = (Integral (M2,(X-vol (E1,M1)))) + (Integral (M2,(X-vol (E2,M1))))