σ-homomorphisms from the Borel σ-algebra into the Loeb σ-algebra

✍ Scribed by Hermann Render

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 103 KB
• Volume: 111
• Category: Article
• ISSN: 0168-0072
• DOI: 10.1016/s0168-0072(01)00032-x

✦ Synopsis

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