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