theorem Th22: :: MEASUR14:22

for X, Y being non empty set
for S being SigmaField of X
for T being Function of X,Y
for f being PartFunc of X,ExtREAL
for g being PartFunc of Y,ExtREAL st T is bijective & g = f * (T ") holds
( f is_simple_func_in S iff g is_simple_func_in CopyField (T,S) )