
theorem Th47:
for X be non empty set, F be Functional_Sequence of X,ExtREAL
 st (for n be Nat holds F.n is without-infty) holds F is additive
proof
  let X be non empty set, F be Functional_Sequence of X,ExtREAL;
  assume for n be Nat holds F.n is without-infty; then
  for n,m be Nat st n <> m for x be set st x in dom(F.n)/\dom(F.m)
    holds (F.n).x <> +infty or (F.m).x <> -infty by MESFUNC5:def 5;
  hence F is additive by MESFUNC9:def 5;
end;
