theorem Th47: :: MESFUN12:47

for X1, X2 being non empty set
for S1 being SigmaField of X1
for S2 being SigmaField of X2
for f being PartFunc of [:X1,X2:],ExtREAL
for x being Element of X1
for y being Element of X2
for E being Element of sigma (measurable_rectangles (S1,S2)) st E c= dom f & f is E -measurable holds
( ProjPMap1 (f,x) is Measurable-X-section (E,x) -measurable & ProjPMap2 (f,y) is Measurable-Y-section (E,y) -measurable )