theorem Th35:
  f in L1_CFunctions M & g in L1_CFunctions M & a.e-Ceq-class(f,M) =
  a.e-Ceq-class(g,M) implies a.e-Ceq-class(a(#)f,M) = a.e-Ceq-class(a(#)g,M)
proof
  assume that
A1: f in L1_CFunctions M & g in L1_CFunctions M and
A2: a.e-Ceq-class(f,M) = a.e-Ceq-class(g,M);
  f a.e.cpfunc= g,M by A1,A2,Th32;
  then
A3: a(#)f a.e.cpfunc= a(#)g,M by Th26;
  a(#)f in L1_CFunctions M & a(#)g in L1_CFunctions M by A1,Th18;
  hence thesis by A3,Th32;
end;
