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Chapter I. Properties of the Apparatus

1. Introduction

2. Convergents

3. Infinite continued fractions

4. Continued fractions with natural elements

Chapter II. The Representation of Numbers by Continued Fractions

5. Continued fractions as an apparatus for representing real numbers

6. Convergents as best approximations

7. The order of approximation

8. General approximation theorems

9. The approximation of algebraic irrational numbers and Liouville's transcendental numbers

10. Quadratic irrational numbers and periodic continued fractions

Chapter III. The Measure Theory of Continued Fractions

11. Introduction

12. The elements as functions of the number represented

13. Measure-theoretic evaluation of the increase in the elements

14. Measure-theoretic evaluation of the increase in the denominators of the convergents. The fundamental theorem of the measure theory of approximation

15. Gauss's problem and Kuz'min's theorem

16. Average values

Index

1. Introduction

2. Convergents

3. Infinite continued fractions

4. Continued fractions with natural elements

Chapter II. The Representation of Numbers by Continued Fractions

5. Continued fractions as an apparatus for representing real numbers

6. Convergents as best approximations

7. The order of approximation

8. General approximation theorems

9. The approximation of algebraic irrational numbers and Liouville's transcendental numbers

10. Quadratic irrational numbers and periodic continued fractions

Chapter III. The Measure Theory of Continued Fractions

11. Introduction

12. The elements as functions of the number represented

13. Measure-theoretic evaluation of the increase in the elements

14. Measure-theoretic evaluation of the increase in the denominators of the convergents. The fundamental theorem of the measure theory of approximation

15. Gauss's problem and Kuz'min's theorem

16. Average values

Index

Library of Congress subject headings for this publication: Continued fractions