theorem Th62: :: MESFUN12:62

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 x being Element of X1
for E being Element of sigma (measurable_rectangles (S1,S2)) st M2 is sigma_finite holds
(Y-vol (E,M2)) . x = Integral (M2,(chi ((Measurable-X-section (E,x)),X2)))