theorem Th96: :: MEASUR11:97

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 E being Element of sigma (measurable_rectangles (S1,S2))
for A being Element of S1
for B being Element of S2 st E = [:A,B:] & M2 is sigma_finite holds
( ( M2 . B = +infty implies Y-vol (E,M2) = Xchi (A,X1) ) & ( M2 . B <> +infty implies ex r being Real st
( r = M2 . B & Y-vol (E,M2) = r (#) (chi (A,X1)) ) ) )