Intersection Numbers and Weak* Separability of Spaces of Measures.
Let be a completely regular space, a boundedly complete vector lattice,
This is an expository paper on Jan Marik's result concerning an extension of a Baire measure to a Borel measure.
We construct two examples of a compact, 0-dimensional space which supports a Radon probability measure whose measure algebra is isomorphic to the measure algebra of . The first construction uses ♢ to produce an S-space with no convergent sequences in which every perfect set is a . A space with these properties must be both hereditarily normal and hereditarily countably paracompact. The second space is constructed under CH and is both HS and HL.
We prove that the statement: "there is a Corson compact space with a non-separable Radon measure" is equivalent to a number of natural statements in set theory.
It is shown that Čech completeness, ultracompleteness and local compactness can be defined by demanding that certain equivalences hold between certain classes of Baire measures or by demanding that certain classes of Baire measures have non-empty support. This shows that these three topological properties are measurable, similarly to the classical examples of compact spaces, pseudo-compact spaces and realcompact spaces.