theorem Th47: :: MEASUR11:52

for X1, X2 being non empty set
for S1 being SigmaField of X1
for S2 being SigmaField of X2
for M2 being sigma_Measure of S2
for A being Element of S1
for B being Element of S2
for x being Element of X1 holds (M2 . B) * ((chi (A,X1)) . x) = Integral (M2,(ProjMap1 ((chi ([:A,B:],[:X1,X2:])),x)))