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;
