Fractals in Probability and Analysis

This book offers a mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities. The clear presentation of a broad range of techniques makes the volume accessible to graduate students, while the independent nature of chapters renders it a useful supplement or resource for a variety of courses.

This is a mathematically rigorous introduction to fractals which emphasizes examples and fundamental ideas. Building up from basic techniques of geometric measure theory and probability, central topics such as Hausdorff dimension, self-similar sets and Brownian motion are introduced, as are more specialized topics, including Kakeya sets, capacity, percolation on trees and the traveling salesman theorem. The broad range of techniques presented enables key ideas to be highlighted, without the distraction of excessive technicalities. The authors incorporate some novel proofs which are simpler than those available elsewhere. Where possible, chapters are designed to be read independently so the book can be used to teach a variety of courses, with the clear structure offering students an accessible route into the topic.

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