theorem Th50: :: MEASUR11:55

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))
for A being Element of S1
for B being Element of S2
for y being Element of X2 st E = [:A,B:] holds
M1 . (Measurable-Y-section (E,y)) = (M1 . A) * ((chi (B,X2)) . y)