Quasi-Radon measures and Radon measures of type (\(\mathcal H\)) (Q804735)

It is well-known that every Radon measure on a topological space (introduced by L. Schwartz in 1973) is a locally finite Radon measure of type (\({\mathcal K})\), \({\mathcal K}\) being the family of all compact subsets of the space. The object of this paper is to state the relations between the quasi-Radon measures (defined by D. H. Fremlin in 1974) and the Radon measures of type (\({\mathcal H})\) (defined by the author in 1973), proving that every quasi-Radon measure is a complete and locally determined Radon measure of type (\({\mathcal F}_ 0)\), where \({\mathcal F}_ 0\) denotes the class of the closed subsets of finite measure, and that every almost everywhere locally finite, complete and locally determined Radon measure of type (\({\mathcal H})\) is a quasi-Radon measure. So there exist Radon measures of type (\({\mathcal H})\) which are not quasi-Radon. It is also possible to find Radon measures of type (\({\mathcal H})\) which are not Radon.