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 x being Element of X1
for y being Element of X2 holds
( ProjPMap1 ((chi (E,[:X1,X2:])),x) = chi ((Measurable-X-section (E,x)),X2) & ProjPMap2 ((chi (E,[:X1,X2:])),y) = chi ((Measurable-Y-section (E,y)),X1) )