Special measures and repleteness (Q689035)

Summary: Let \(X\) be an abstract set and \({\mathcal L}\) a lattice of subsets of \(X\). To each lattice-regular measure \(\mu\) we associate two induced measures \(\hat\mu\) and \(\tilde\mu\) on suitable lattices of the Wallman space \(I_ R({\mathcal L})\) and another measure \(\mu'\) on the space \(I^ \sigma_ R({\mathcal L})\). We investigate the reflection of smoothness properties of \(\mu\) onto \(\hat\mu\), \(\tilde\mu\) and \(\mu'\) and give some new criterion for repleteness and measure repleteness.