theorem Th108: :: MEASUR11:108

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, V being Element of sigma (measurable_rectangles (S1,S2))
for P being Set_Sequence of sigma (measurable_rectangles (S1,S2))
for x being Element of X1 st P is non-descending & lim P = E holds
ex K being SetSequence of S2 st
( K is non-descending & ( for n being Nat holds K . n = (Measurable-X-section ((P . n),x)) /\ (Measurable-X-section (V,x)) ) & lim K = (Measurable-X-section (E,x)) /\ (Measurable-X-section (V,x)) )