reserve X for non empty set,
  Y for set,
  S for SigmaField of X,
  M for sigma_Measure of S,
  f,g for PartFunc of X,COMPLEX,
  r for Real,
  c for Complex,
  E,A,B for Element of S;

theorem
  dom f = A implies (f is B-measurable iff f is (A/\B)-measurable)
proof
  assume
A1: dom f = A;
  then
A2: dom Re f = A by COMSEQ_3:def 3;
A3: dom Im f = A by A1,COMSEQ_3:def 4;
  hence f is B-measurable implies f is (A/\B)-measurable by A2,MESFUNC6:80;
  thus thesis by A2,A3,MESFUNC6:80;
end;
