Probability measures with big kernels (Q2761598)

Let \(\mu\) be a probability measure on a topological vector space \(X\) and let \(\tau_{\mu}\) be the topology in \(X^*\) of convergence in measure \(\mu\). The kernel \(\mathcal{H}_{\mu}\) of \(\mu\) is defined as the dual space of \((X^*,\tau_{\mu})\). The authors investigate how big is \(\mathcal{H}_{\mu}\). For example (one of the main results), if \(X\) is an infinite-dimensional space of second category and the dual \(X^*\) separates points of \(X\), then \(\mathcal{H}_{\mu}\cap X\neq X\).