(** ** Limits, integrals and differentiability *)

Definition is_connected (D : R -> Prop) :=
  forall a b x, D a -> D b -> a <= x <= b -> D x.

Lemma CVN_CVU_r (fn : nat -> R -> R) (r : posreal) : CVN_r fn r -> forall x, (Rabs x < r) -> exists e : posreal, CVU (fun n => SP fn n) (fun x => Series (fun n => fn n x)) x e.