theorem :: MESFUN13:29

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 x being Element of X1 holds
( ( M2 . (Measurable-X-section (E,x)) <> 0 implies (Integral2 (M2,(Xchi (E,[:X1,X2:])))) . x = +infty ) & ( M2 . (Measurable-X-section (E,x)) = 0 implies (Integral2 (M2,(Xchi (E,[:X1,X2:])))) . x = 0 ) )