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Smaug123 comments on The Best Textbooks on Every Subject - Less Wrong

167 Post author: lukeprog 16 January 2011 08:30AM

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Comment author: Smaug123 05 April 2016 09:23:36PM 2 points [-]

On introductory non-standard analysis, Goldblatt's "Lectures on the hyperreals" from the Graduate Texts in Mathematics series. Goldblatt introduces the hyperreals using an ultrapower, then explores analysis and some rather complicated applications like Lebesgue measure.

Goldblatt is preferred to Robinson's "Non-standard analysis", which is highly in-depth about the specific logical constructions; Goldblatt doesn't waste too much time on that, but constructs a model, proves some stuff in it, then generalises quite early. Also preferred to Hurd and Loeb's "An introduction to non-standard real analysis", which I somehow just couldn't really get into. Its treatment of measure theory, for instance, is just much more difficult to understand than Goldblatt's.