theorem Th79: :: MEASUR11:80

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)) st E in Field_generated_by (measurable_rectangles (S1,S2)) holds
for B being Element of S1 holds E in { E where E is Element of sigma (measurable_rectangles (S1,S2)) : ex F being Function of X2,ExtREAL st
( ( for x being Element of X2 holds F . x = M1 . ((Measurable-Y-section (E,x)) /\ B) ) & ( for V being Element of S2 holds F is V -measurable ) ) }