I believe the following book by Yakov Sinai: "Probability Theory An Introductory Course" (Springer) uses such an argument to proove a version of the central limit theorem in chaper 15. UPDATE A better reference is the updated verson of that book, Leonid Koralov, Yakov Sinai: "Theory of Probability and Random Prosecces, second edition" (Universitext).

I believe the following book by Yakov Sinai: "Probability Theory An Introductory Course" (Springer) uses such an argument to prove a version of the central limit theorem in chapter 15. UPDATE A better reference is the updated version of that book, Leonid Koralov & Yakov Sinai: "Theory of Probability and Random Processes, second edition"   (Universitext).

I believe the following book by Yakov Sinai: "Probability Theory An Introductory Course" (Springer) uses such an argument to proove a version of the central limit theorem in chaper 15.

I believe the following book by Yakov Sinai: "Probability Theory An Introductory Course" (Springer) uses such an argument to proove a version of the central limit theorem in chaper 15. UPDATE A better reference is the updated verson of that book, Leonid Koralov, Yakov Sinai: "Theory of Probability and Random Prosecces, second edition" (Universitext).