 reserve a,b,r for Complex;
 reserve V for ComplexLinearSpace;
reserve A,B for non empty set;
reserve f,g,h for Element of PFuncs(A,COMPLEX);
reserve u,v,w for VECTOR of CLSp_PFunctA;
reserve X for non empty set,
  x for Element of X,
  S for SigmaField of X,
  M for sigma_Measure of S,
  E,E1,E2,A,B for Element of S,
  f,g,h,f1,g1 for PartFunc of X,COMPLEX;
reserve v,u for VECTOR of CLSp_L1Funct M;
reserve v,u for VECTOR of CLSp_AlmostZeroFunct M;

theorem
  f in L1_CFunctions M & g in L1_CFunctions M implies (a.e-Ceq-class(f,M) =
  a.e-Ceq-class(g,M) iff g in a.e-Ceq-class(f,M))
proof
  assume
A1: f in L1_CFunctions M & g in L1_CFunctions M;
  then g a.e.cpfunc= f,M iff g in a.e-Ceq-class(f,M) by Th30;
  hence thesis by A1,Th32;
end;
