The Metrical Theory of Jacobi-Perron Algorithm
| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1973, 1973
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| Edition: | 1st ed. 1973 |
| Series: | Lecture Notes in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- Basic definitions
- Cylinders
- Increasing ?-fields
- Conditional expectations
- Ergodicity of the transformation
- Existence of an equivalent invariant measure
- The ergodic theorem
- Kuzmin's Theorem
- Convergence results
- The Borel-Cantelli lemma of Schmidt-Philipp
- Some extensions of Kuzmin's theorem
- Outer measures
- Hausdorff measures
- Hausdorff dimension
- Billingsley dimension
- Comparison theorems
- The main theorem of dimension theory of Jacobi algorithm
- Ergodic invariant measures
- Volume as approximation measure
- Proof of the conjecture for n=1 and n=2
- The metrical theory of Jacobi-Perron algorithm
- Errata