This book contains a selection of classical mathematical papers related to fractal geometry. It is intended for the convenience of the student or scholar wishing to learn about fractal geometry.
Introduction 1. On Continuous Functions of a Real Argument that do not have a Well-Defined Differential Quotient 2. On the Power of Perfect Sets of Points 3. On a Continuous Curve without Tangent Constructible from Elementary Geometry 4. On the linear Measure of Point Sets—a Generalization 5. Dimension and Outer Measure 6. General Spaces and Cartesian Spaces 7. Improper Sets and Dimension Numbers (excerpt) 8. On a Metric Property of Dimension 9. On the Sum of Digits of Real Numbers Represented in the Dyadic System (1934) 10. On Rational Approximations to Real Numbers (1934) 11. On Dimensional Numbers of Some Continuous Curves (1937) 12. Plane or Space Curves and Surfaces Consisting of Parts Similar to the Whole 13. Additive Functions of Intervals and Hausdorff Measure (1946) 14. The Dimension of Cartesian Product Sets (1954) 15. On the Complementary Intervals of a Linear Closed Set of Zero Lebesgue Measure (1954) 16. On Some Curves Defined by Functional Equations (1957) 17. e-Entropy and e-Capacity of Sets in Functional Spaces (excerpt) 18. A Simple Example of a Function which is Everywhere Continuous and Nowhere Differentiable 19. How Long is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension (1967)