theorem Th42: :: MEASUR11:47

for X1, X2 being non empty set
for S1 being SigmaField of X1
for S2 being SigmaField of X2
for E being Element of sigma (measurable_rectangles (S1,S2))
for K being set st K = { C where C is Subset of [:X1,X2:] : for p being set holds X-section (C,p) in S2 } holds
( Field_generated_by (measurable_rectangles (S1,S2)) c= K & K is SigmaField of [:X1,X2:] )