Integration with Hyperreals
I've recently, for no particular reason, gotten interested in the basics of nonstandard analysis. One of the better articles I've found is at the Ask Dr. Math website, but in this section only mentions that nonstandard integrals are more difficult and use the transfer principle more.
What I want to know is exactly how integrals work in nonstandard analysis (that is, what exactly is the definition, and how can it be used to prove the fundamental theorem(s) of calculus?). I haven't had much luck searching online for a good account of this.
What I want to know is exactly how integrals work in nonstandard analysis (that is, what exactly is the definition, and how can it be used to prove the fundamental theorem(s) of calculus?). I haven't had much luck searching online for a good account of this.