reserve n,k for Nat,
  X for non empty set,
  S for SigmaField of X;

theorem Th3:
  for M be sigma_Measure of S, F be SetSequence of S
  ex G be sequence of S st
  G = inferior_setsequence F & M.(lim_inf F) = sup rng(M*G)
proof
  let M be sigma_Measure of S, F be SetSequence of S;
  rng inferior_setsequence F c= S;
  then reconsider G = inferior_setsequence(F) as sequence of S by FUNCT_2:6;
  for n being Nat holds G.n c= G.(n+1) by PROB_1:def 5,NAT_1:12;
  then M.(union rng G)= sup rng(M*G) by MEASURE2:23;
  hence thesis;
end;
