Sample Sections from a Comprehensive Course in Analysis by Barry Simon

This is a supplementary page to a basic page on a set of five books by Barry Simon.  This has links to ten sample sections, two from each part.

Part 1 Real Analysis. 
Section 3.5 Classical Fourier Series
Section 7.2 Borel–Cantelli Lemmas and the Laws of Large Numbers and of the Iterated Logarithm

Part 2a Basic Complex Analysis.
Section 3.1 Analyticity and Cauchy Estimates (part of a Chapter on Consequences of the Cauchy Integral Formula)
Section 9.6 The Gamma Function: Basics

Part 2b Advanced Complex Analysis.
Section 13.4 Dirichlet's Prime Progression Theorem
Section 15.4 The Method of Steepest Descent

Part 3 Harmonic Analysis.
Section 2.8 Bonus Section: More Applications of the Ergodic Theorems (Skew shifts, Continued fractions, Geodesic flow)
Section 4.6 Wavelets

Part 4 Operator Theory.
Section 2.4 The Square Root Lemma and the Polar Decomposition
Section 6.9 Bonus Section: Fourier Analysis on LCA Groups