theorem Th4: :: MESFUN13:12

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 U being Element of S1
for f being b₆ -measurable PartFunc of [:X1,X2:],ExtREAL st M2 is sigma_finite & E = dom f holds
Integral2 (M2,|.f.|) is U -measurable