reserve X for non empty set,
  S for SigmaField of X,
  M for sigma_Measure of S,
  E for Element of S,
  F for Functional_Sequence of X,REAL,

  f for PartFunc of X,REAL,
  seq for Real_Sequence,
  n,m for Nat,
  x for Element of X,
  z,D for set;
reserve i for Element of NAT;

theorem Th10:
  dom((Partial_Sums F).n) = meet{dom(F.k) where k is Element of NAT : k <= n}
proof
  dom((Partial_Sums R_EAL F).n) = meet{dom((R_EAL F).k) where k is Element
of NAT : k <= n} & (Partial_Sums R_EAL F).n = (R_EAL(Partial_Sums F)).n by Th7
,Th9,MESFUNC9:28;
  hence thesis;
end;
