Short introduction to Nonstandard Analysis

Abstract

These lecture notes, to be completed in a later version, offer a short and rigorous introduction to Nostandard Analysis, mainly aimed to reach to a presentation of the basics of Loeb integration, and in particular, Loeb measures. The Abraham Robinson version of Nostandard Analysis is pursued, with a respective incursion into Superstructures. Two formal languages are used, one simpler at first, and then later, one for the full blown theory. A number of detailed comments, not often found in textbooks, accompanies the text.