Contents

1 Introduction

2 Preliminaries

2.1 Hausdorff measures and dimension  
2.2 Dimension of measures  
2.3 Multifractal analysis of measures  
2.4 Iterated function systems and self-similar measures  
2.5 The open set condition  
2.6 Hausdorff dimension of self-similar sets  
2.7 Singular Value Function  

3 The "original" Mass Transference Principle and the Duffin–Schaeffer Conjecture

4 Precursors to the Mass Transference Principle

5 Mass Transference Principle for Systems of Linear Forms

6 Mass Transference Principle with "Local Scaling Property"

7 Mass Transference Principle from Balls to Rectangles

8 Mass Transference Principles from Rectangles to Rectangles

9 Mass Transference Principles from Balls to Open Sets

10 Mass Transference Principles for Inhomogeneous Measures