theorem Th80: :: MEASUR11:81

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 B being Element of S2 holds Field_generated_by (measurable_rectangles (S1,S2)) c= { E where E is Element of sigma (measurable_rectangles (S1,S2)) : ex F being Function of X1,ExtREAL st
( ( for x being Element of X1 holds F . x = M2 . ((Measurable-X-section (E,x)) /\ B) ) & ( for V being Element of S1 holds F is V -measurable ) ) }