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May I get some recommendation on text book on real analysis for undergrad in statistics? Thank you.

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  • $\begingroup$ Are you looking for a book that treats measure theory from a stats perspective, or a mathematical stats book that has a focus on real analysis? Also, is this a book for self-study to supplement for a student in a class, or will you be using it as the teacher, etc? It might be helpful to know the book's particular purpose. $\endgroup$ – Nick C Oct 5 '17 at 23:49
  • $\begingroup$ The standard for real analysis is Walter Rudin's "Principles of Mathematical Analysis". I didn't get that as an undergraduate, and feel that I partly wasted a few decades by not getting it. $\endgroup$ – Daniel R. Collins Oct 5 '17 at 23:52
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Maybe this would be more useful "for [an] undergrad in statistics" than a text on pure real analysis? A review in an ASA journal says it is "user-friendly":

Adams, Malcolm Ritchie, and Victor Guillemin. Measure theory and probability. Boston: Birkhäuser, 1996.


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"…the text is user friendly to the topics it considers and should be very accessible…Instructors and students of statistical measure theoretic courses will appreciate the numerous informative exercises; helpful hints or solution outlines are given with many of the problems. All in all, the text should make a useful reference for professionals and students."—The Journal of the American Statistical Association

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