theorem
  for X,S,f,A,B st f is A-measurable & f is B-measurable holds
  f is (A \/ B)-measurable
proof
  let X,S,f,A,B;
  assume
A1: f is A-measurable & f is B-measurable;
 for r being Real holds ((A \/ B) /\ less_dom(f,r)) in S
  proof
    let r be Real;
    A /\ less_dom(f,r) in S & B /\ less_dom(f,r) in S by A1;
    then (A /\ less_dom(f,r)) \/ (B /\ less_dom(f,r)) in S by FINSUB_1:def 1;
    hence thesis by XBOOLE_1:23;
  end;
  hence thesis;
end;
