Is there any good text introducing a part of Borel-hierarchy which is in need in measure theory Is there any good text introducing a subpart of Borel-hierarchy which is in need in measure theory, which can be done in short time? Say, 1~3 days if possible. (Assuming I'm studying about 14hours a day) 
To be more precise, I want to learn that "The Sigma-algebra generated by a set $S$" is exactly $\bigcup_{\alpha<\omega_1} \prod_{\alpha}^0$
 A: Foran's book and Goffman's book are especially good for what you want, while Bruckner/Bruckner/Thomson's book, Natanson's book, Cohn's book, Billingsley's book, and Vestrup's book all have more than the average amount (for a real analysis text) on Borel sets. Hrbacek/Jech's book and Devlin's book both have relatively elementary treatments of the hierarchy result. Finally, there's a chapter in Laczkovich's book on Borel sets that is very good for an initial encounter with them.
Fundamentals of Real Analysis by James Foran
Real Functions by Casper Goffman
[Real Analysis] by Bruckner/Bruckner/Thomson (google for a freely available digital copy)
Theory of Functions of a Real Variable (Volume 2) by Isidor P. Natanson
Measure Theory by Donald L. Cohn
Probability and Measure by Patrick Billingsley
The Theory of Measures and Integration by Eric M. Vestrup
Introduction to Set Theory by Hrbacek/Jech
The Joy of Sets. Fundamentals of Contemporary Set Theory by Keith Devlin
Conjecture and Proof by Miklós Laczkovich
(ADDED NEXT DAY) I don't know how I forgot about Rooij/Schikhof's book below. I rank it with Foran's and Goffman's book as real analysis texts that I think would be most useful for what you want:
A Second Course on Real Functions by A. C. M. van Rooij and W. H. Schikhof
