reserve X for set;

theorem
  for S being SigmaField of X, M being sigma_Measure of S, T being
N_Measure_fam of S st (for A being set st A in T holds A is measure_zero of M)
  holds meet T is measure_zero of M
proof
  let S be SigmaField of X, M be sigma_Measure of S, T be N_Measure_fam of S;
  assume
A1: for A being set holds A in T implies A is measure_zero of M;
  ex A being set st A in T & A is measure_zero of M
  proof
    consider F being sequence of bool X such that
A2: T = rng F by SUPINF_2:def 8;
    take F.0;
    thus thesis by A1,A2,FUNCT_2:4;
  end;
  hence thesis by MEASURE1:36,SETFAM_1:3;
end;
