theorem Th54:
  Integral(M,abs(X-->0)) = 0
proof
  set f=X --> 0;
A1: now
    let x be Element of X;
    f.x = 0 by FUNCOP_1:7;
    then
A2: |.f.x qua Complex.| = 0 by ABSVALUE:2;
    assume x in dom abs f;
    hence (abs f).x = 0 by A2,VALUED_1:def 11;
  end;
  dom f = X by FUNCOP_1:13;
  then dom abs f = X by VALUED_1:def 11;
  hence thesis by A1,Lm2;
end;
