ABSTRACT

Read the masters! Experience has shown that this is good advice for the serious mathematics student. This book contains a selection of the classical mathematical papers related to fractal geometry. For the convenience of the student or scholar wishing to learn about fractal geometry, nineteen of these papers are collected here in one place. Twelve of the nineteen have been translated into English from German, French, or Russian. In many branches of science, the work of previous generations is of interest only for historical reasons. This is much less so in mathematics.1 Modern-day mathematicians can learn (and even find good ideas) by reading the best of the papers of bygone years. In preparing this volume, I was surprised by many of the ideas that come up.

chapter Two|14 pages

On the Power of Perfect Sets of Points

chapter Five|27 pages

Dimension and Outer Measure

chapter Six|15 pages

General Spaces and Cartesian Spaces

chapter Nine|16 pages

On the Sum of Digits of Real Numbers Represented in the Dyadic System

(On sets of fractional dimensions II.)

chapter Fourteen|9 pages

The Dimension of Cartesian Product Sets