| Preface | v |
| 1. | Fractal Measures | 1 |
| 1.1 | Measure Theory | 1 |
| 1.2 | Hausdorff and Packing Measures | 13 |
| 1.3 | Vitali Theorems | 21 |
| 1.4 | Other Local Fractal Measures | 28 |
| 1.5 | Geometry of Fractals | 41 |
| 1.6* | Ultrametric Spaces | 54 |
| 1.7* | Comparable Net Measures | 58 |
| 1.8* | Remarks | 63 |
| 2. | Integrals | 69 |
| 2.1 | Product Measures | 69 |
| 2.2 | Integrals | 77 |
| 2.3 | Radon-Nikodym Theorem | 88 |
| 2.4 | Measures as Linear Functionals | 93 |
| 2.5 | Spaces of Measures | 100 |
| 2.6* | Remarks | 109 |
| 3. | Integrals and Fractals | 113 |
| 3.1* | Topological and Fractal Dimension | 113 |
| 3.2 | Potential Theory | 115 |
| 3.3 | Fractal Measures | 123 |
| 3.4 | Self-Affine Graphs | 135 |
| 3.5* | Graph Self-Similar Measures | 146 |
| 3.6* | Remarks | 148 |
| 4. | Probability | 153 |
| 4.1 | Events | 153 |
| 4.2 | Random Variables | 158 |
| 4.3 | Dependence | 175 |
| 4.4 | Limit Theorems | 195 |
| 4.5* | Remarks | 201 |
| 5. | Probability and Fractals | 203 |
| 5.1 | The Chaos Game | 203 |
| 5.2 | Dimension of Self-Similar Measures | 208 |
| 5.3 | Random Cantor Sets | 213 |
| 5.4 | Statistical Self-Similarity | 220 |
| 5.5 | Statistically Self-Affine Graphs | 230 |
| 5.6 | Brownian Motion | 249 |
| 5.7* | A Multifractal Decomposition | 257 |
| 5.8* | Remarks | 262 |
| References | 267 |
| Notation | 279 |
| Index | 281 |
| | *Asterisks indicate optional sections. |