Fractals in probability and analysis / Christopher J. Bishop and Yuval Peres.

Includes bibliographical references and index.

1. Minkowski and Hausdorff dimensions;
2. Self-similarity and packing dimension;
3. Frostman's theory and capacity;
4. Self-affine sets;
5. Graphs of continuous functions;
6. Brownian motion, part I;
7. Brownian motion, part II;
8. Random walks, Markov chains and capacity;
9. Besicovitch-Kakeya sets;
10. The traveling salesman theorem;
Appendix A. Banach's fixed-point theorem;
Appendix B. Frostman's lemma for analytic sets;
Appendix C. Hints and solutions to selected exercises; References;
Index.

A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.