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