theorem Th48: :: MEASUR11:53

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 E being Element of sigma (measurable_rectangles (S1,S2))
for A being Element of S1
for B being Element of S2
for x being Element of X1 st E = [:A,B:] holds
M2 . (Measurable-X-section (E,x)) = (M2 . B) * ((chi (A,X1)) . x)