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 CCommented Oct 5, 2017 at 23:49
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$\begingroup$ 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. CollinsCommented Oct 5, 2017 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.
"…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
answered Oct 5, 2017 at 23:54