TY  - BOOK
AU  - Vallin,Robert W.
TI  - Elements of Cantor sets - with applications
SN  - 9781118405710 
U1  - 515.8 23
PY  - 2013///
CY  - New Jersey : 
PB  - John Wiley & Sons
KW  - Cantor, George.
KW  - Cantor sets
KW  - Measure theory
KW  - Mathematical analysis
N1  - Includes bibliographical references and index; 1. Quick Biography of Cantor --
2. Basics --
3. Introducing the Cantor Set --
4. Cantor Sets and Continued Fractions --
5. p-adic Numbers and Valuations --
6. Self-Similar Objects --
7. Various Notions of Dimension --
8. Porosity and Thickness-Looking at the Gaps --
9. Creating Pathological Functions via C --
10. Generalizations and Applications --
11. Epilogue
N2  - "This book is a thorough introduction to the Cantor (Ternary) Set and its applications and brings together many of the topics (advanced calculus, probability, topology, and algebra) that mathematics students are required to study, but unfortunately are treated as separate ideas. This book successfully bridges the gap between how several mathematical fields interact using Cantor Sets as the common theme.  While the book is mathematically self-contained, readers should be comfortable with mathematical formalism and have some experience in reading and writing mathematical proofs.  Chapter coverage includes: a biography of Cantor; an introduction to the Cantor (Ternary) Set; Self-Similar Sets and Fractal Dimensions; sums of Cantor Sets; the role of Cantor Sets to create pathological functions; and additional topics such as continued fractions, Ana Sets, and p-adic numbers"--
ER  -