
theorem
for A1 be Element of Borel_Sets, A2 be Element of L-Field,
 f be PartFunc of REAL,ExtREAL
 st A1 = A2 & f is A1-measurable holds f is A2-measurable
proof
    let A1 be Element of Borel_Sets, A2 be Element of L-Field,
    f be PartFunc of REAL,ExtREAL;
    assume that
A1:  A1 = A2 and
A2:  f is A1-measurable;
    for r be Real holds A2 /\ less_dom(f,r) in L-Field
      by A1,A2,MESFUNC1:def 16,MEASUR12:75;
    hence f is A2-measurable by MESFUNC1:def 16;
end;
