Zahle Martina. Lectures on Fractal Geometry

World Scientific Pub Co Inc, 2024. — 134 p. — ISBN-13: 978-981-128-333-8.This book is based on a series of lectures at the Mathematics Department of the University of Jena, developed in the period from 1995 up to 2015. It is completed by additional material and extensions of some basic results from the literature to more general metric spaces.This book provides a clear introduction to classical fields of fractal geometry, which provide some background for modern topics of research and applications. Some basic knowledge on general measure theory and on topological notions in metric spaces is presumed.Preface
About the Author
Acknowledgments
Measure Theoretic Foundations
Hausdorff and Packing Measures
Upper and Lower Densities of Measures and Comparison with Hausdorff and Packing Measures
Hausdorff Dimension and Potential Theory
Other Fractal Dimensions
Dimensions of Borel Measures
Attractors of Iterated Function Systems
An Example from the Theory of Dynamical Systems
Graphs of Functions and Stochastic Processes
Bibliography
Index
Nomenclature