Fractals in Probability and Analysis

ISBN-13: 9781107134119 / Angielski / Twarda / 2016 / 412 str.

Bishop, Christopher|||Peres, Yuval

Opis

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

Recenzje

'This is a technical monograph suited to practioners of geometric measure theory and analysis written by two of the world's leaders in the field. It would make a serious study for graduate students, containing a large number of helpful examples.' Chris Athorne, Contemporary Physics

Spis treści

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.