theorem Th64: :: MESFUN12:64

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 E being Element of sigma (measurable_rectangles (S1,S2)) st M1 is sigma_finite holds
X-vol (E,M1) = Integral1 (M1,(chi (E,[:X1,X2:])))