\(BV\) as a dual space (Q2568668)

The authors prove that the normed vector space \(BV\) of games with bounded variation on a field \(\mathcal C\) is the topological dual of the linear space of games \(X\) with finite support endowed with an adequate norm. In fact, this norm is the restriction of the dual norm on \(BV^{\prime}\) when \(X\) is seen as a subspace of \(BV^{\prime}\).