 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 Th30:
  f in L1_CFunctions M & g in L1_CFunctions M implies (g a.e.cpfunc= f,M
  iff g in a.e-Ceq-class(f,M))
proof
  assume
A1: f in L1_CFunctions M & g in L1_CFunctions M;
  hereby
    assume g a.e.cpfunc= f,M;
    then f a.e.cpfunc= g,M;
    hence g in a.e-Ceq-class(f,M) by A1;
  end;
    assume g in a.e-Ceq-class(f,M);
    then ex r be PartFunc of X,COMPLEX st g=r & r in L1_CFunctions M & f in
    L1_CFunctions M & f a.e.cpfunc= r,M;
    hence g a.e.cpfunc= f,M;
end;
