theorem Th67: :: MEASUR11:71

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 M2 being sigma_Measure of S2
for E being Element of sigma (measurable_rectangles (S1,S2))
for x being Element of X1
for y being Element of X2
for U being Element of S1
for V being Element of S2 holds
( M1 . ((Measurable-Y-section (E,y)) /\ U) = Integral (M1,(ProjMap2 ((chi ((E /\ [:U,X2:]),[:X1,X2:])),y))) & M2 . ((Measurable-X-section (E,x)) /\ V) = Integral (M2,(ProjMap1 ((chi ((E /\ [:X1,V:]),[:X1,X2:])),x))) )