Stein: 

Ergodicity: Page 292-306

Dirichlet principle: Page 229-Page253

Hausdorff dimension of Cantor set, Sierpinski Carpet and Kock snowflake: Page 330-341

Besicovitch Sets: Page 360-380

The Brunn-Minkowski inequality and the isoperimetric inequality: Page 34-37 and page 134-145

The Fourier Transform on L1 and L2 spaces: page 96-89, 207-213


Other topics:
 
Rearrangement Inequalities

Haar measure

Sard's theorem

Vector-valued integrals

Riesz-Thorin interpolation