theorem Th22:
  for X be set, S be SigmaField of X, SSets be SetSequence of S, M
  be Function of S,ExtREAL holds M * SSets is ExtREAL_sequence
proof
  let X be set;
  let S be SigmaField of X;
  let SSets be SetSequence of S;
  let M be Function of S,ExtREAL;
  rng SSets c= S;
  then rng SSets c= dom M by FUNCT_2:def 1;
  then dom(M * SSets) = dom SSets by RELAT_1:27;
  then dom(M * SSets) = NAT by FUNCT_2:def 1;
  hence thesis by FUNCT_2:def 1;
end;
