theorem Th50: :: MEASUR14:50

for f1 being PartFunc of [:REAL,REAL:],ExtREAL
for f2 being PartFunc of (CarProduct ((Seg 2) --> REAL)),ExtREAL
for A1 being Element of sigma (measurable_rectangles (L-Field,L-Field))
for A2 being Element of Prod_Field (L-Field 2) st f1 = f2 & A1 = A2 holds
( f1 is A1 -measurable iff f2 is A2 -measurable )