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an12
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Nonstandard analysis in probability theory

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

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?
an12
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