Exercise 27, § 2

Let m be a vectorial measure on T with values in a Hausdorff locally convex space F.

a) Show that if the support of m is finite, then $m = \sum_{i=1}^n c_i \varepsilon_{a_i}$, where the $c_i \in F$.

b) If F is a Banach space, and m is continuous for the topology of compact convergence, show that m has compact support.

c) Give an example of a measure with values in $\mathbf{R}^N$, with noncompact support, that is continuous for the topology of compact convergence.