I was wondering what is a good source / reference to study probability theory with proofs of the CLT and Berry-Esseen Theorems? I am pretty well-versed in the foundations of measure theory but less so in probability (i.e. stuff like characteristic functions, moments, etc) so if there's a text that suits my specific pre-requisite well please let me know, thanks!
Most graduate level texts on probability will prove some flavor of CLT. There is one text I know of that also proves Berry-Esseen:
“Probability Theory” by Alexander Borokov