Section Continuity.
Context {V : NormedModule R_AbsRing}.
End Continuity.

Lemma ex_RInt_locally {V : CompleteNormedModule R_AbsRing} (f : R -> V) (a b : R) :
ex_RInt f a b
-> (exists eps : posreal, ex_RInt f (a - eps) (a + eps))
-> (exists eps : posreal, ex_RInt f (b - eps) (b + eps))
-> locally (a,b) (fun z : R * R => ex_RInt f (fst z) (snd z)).