I was wondering what is a good text that covers topics on probability and Central Limit Theorem for independent but not identically distributed random variables? More specifically, I am pretty well-versed in measure theory and would love to read a probability text with a similar exposition style as Folland (Real Analysis and Their Applications). Unfortunately, Folland's text only covers the classical CLT where random variables are i.i.d.
Somebody previously suggested Borovkov's Probability Theory as a reference but I found the book to be filled with typos and quite difficult digest. Any suggestion is appreciated!