I am quite new at nonstandard analysis, and recently I became aware of its use in probability theory mainly through the following two books: 

 - [Nelson (1987). Radically Elementary Probability Theory][1]
 - [Geyer (2007). Radically Elementary Probability and Statistics][2]

The second one is a draft for a book to be published on some later date.

Although Nelson's book is several decades old, and as far as I can see, its approach has not yet caught on. Also, I couldn't find a lot of papers published in probability journals on that topic. I am quite intrigued by that phenomenon. My question is

 - Why hasn't nonstandard analysis been widely adopted by probabilists? Are there some fundamental objections in probability theory to the approach in there?

  [1]: https://web.math.princeton.edu/~nelson/books/rept.pdf
  [2]: http://www.stat.umn.edu/geyer/nsa/o.pdf