I am currently planning to get a book on Real Analysis for self
studying before diving into my 4th year real analysis course.
The standard textbook for my 4th year course is Stein's Measure,
but I do not like much about abstract measure introduced near the end.
Perhaps because I am currently taking 3rd year real analysis course
in the level of Pugh with some other additional materials.
Anyway, I am considering one of the followings:
Folland – Real Analysis,
Bruckner, Bruckner, Thomson – Real Analysis,
Yeh – Real Analysis,
Kantorovitz – Introduction to Modern Analysis
(and maybe Cohn – Measure Theory)
(Note: Royden is omitted because I am waiting for 2nd printing
and waiting so that I can get it cheap from some website
(like abebooks), so 12 pages of erratas are all fixed)
Which book do you think is most suitable for self-study?
(My 4th year course is cross-listed, meaning it is equivalent to first year graduate real analysis course)
Best Answer
If you want an interesting alternative that goes deep into why things work out as they do in real analysis, especially things like sound and convincing explanations of Lebesgue Measure, then take a look at Terence Tao's 2-volume Analysis textbook.