theorem :: MESFUN13:28

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 y being Element of X2 holds
( ( M1 . (Measurable-Y-section (E,y)) <> 0 implies (Integral1 (M1,(Xchi (E,[:X1,X2:])))) . y = +infty ) & ( M1 . (Measurable-Y-section (E,y)) = 0 implies (Integral1 (M1,(Xchi (E,[:X1,X2:])))) . y = 0 ) )