theorem Th97: :: MEASUR11:98

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:] & M1 is sigma_finite holds
( ( M1 . A = +infty implies X-vol (E,M1) = Xchi (B,X2) ) & ( M1 . A <> +infty implies ex r being Real st
( r = M1 . A & X-vol (E,M1) = r (#) (chi (B,X2)) ) ) )