reserve X for non empty set,
  Y for set,
  S for SigmaField of X,
  F for sequence of S,
  f,g for PartFunc of X,REAL,
  A,B for Element of S,
  r,s for Real,
  a for Real,
  n for Nat;
reserve X for non empty set,
  S for SigmaField of X,
  f,g for PartFunc of X,REAL,
  A for Element of S,
  r for Real,
  p for Rational;
reserve X for non empty set,
  f,g for PartFunc of X,REAL,
  r for Real ;
reserve X for non empty set,
  S for SigmaField of X,
  f,g for PartFunc of X,REAL,
  A for Element of S;

theorem
  f is A-measurable & A c= dom f implies abs f is A-measurable
proof
  assume that
A1: f is A-measurable and
A2: A c= dom f;
  R_EAL f is A-measurable by A1;
  then |.R_EAL f.| is A-measurable by A2,MESFUNC2:27;
  then R_EAL(abs f) is A-measurable by Th44;
  hence thesis;
end;
