theorem Th61: :: MESFUN12:61

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 y being Element of X2
for E being Element of sigma (measurable_rectangles (S1,S2)) st M1 is sigma_finite holds
(X-vol (E,M1)) . y = Integral (M1,(chi ((Measurable-Y-section (E,y)),X1)))