A topological characterisation of Haar null convex Sets

In R d \mathbb {R}^d , a closed, convex set has zero Lebesgue measure if and only its interior is empty. More generally, in separable, reflexive Banach spaces, closed sets are Haar null their We extend this facts by showing that separable space weak /> ∗ encoding="application/x-tex">^* closure the second dual empty with respect to norm topology. It then follows that, metric of all nonempty, bounded subsets space, converging sequences have limits.