ABSTRACT
This chapter aims to describe some ramifications for both standard and nonstandard measure theory, and to point out some interesting open questions connected to the result. The reader is assumed to be familiar with nonstandard analysis in general, and P. A. Loeb measures in particular, and is referred to or for background. In a different context, C. W. Henson constructed a horribly nonmeasurable set as a counterexample to a question about unbounded Loeb measures. The construction appeals directly to the details of a specific nonstandard model; the question naturally arose whether this example could be constructed in a model satisfying IPκ for some κ. The chapter shows that IPκ suffices for the Henson example as well; in addition, the authors find a nice reformulation of IPκ which should make it easy to use on an everyday basis.
