σ-homomorphisms from the Borel σ-algebra into the Loeb σ-algebra Original Research Article

In nonstandard measure theory the standard part map is very useful to represent standard measures by Loeb measures. We give here a different method of representing measures using the concept of a σ-homomorphism. As an application a measure extension theorem is derived. Finally a nonstandard proof of a result of Pták is given showing that his assumption of nonmeasurable cardinality is redundant.