| Abstract: | Summary In this paper, the principal role is played by the adjoint of a certain bounded linear mapping, whose domain and range are Banach spaces of lattice regular measures. First, the general properties of the adjoint are investigated and it is shown, in particular, how this mapping yields generalizations of many results in Stone- ech Theory, especially matters related to embeddibility. Then, the investigation continues with the mapping properties of the adjoint, and a variety of applications is given to Topological Measure Theory, strong measure repleteness, tightness, and relative compactness. |
