Strictly nonzero charges. (Q1415004)

Let \(\mathcal A\) be a Boolean algebra and \(G\) be a group. The authors study the problem when there exists a charge (i.e., a finitely additive measure) \(\mu:{\mathcal A}\to G\) which is strictly nonzero in the sense that \(\mu(A)\neq 0\) whenever \(A\in{\mathcal A}\) and \(A\neq \emptyset\). Special attention is paid to the case \(G=\mathbb{Z}\) and to the case of \(\mathcal A\) being the algebra of clopen subsets of the product space \(2^Y\).