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Beschreibung
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.
Details
| Verlag | Springer Berlin |
| Ersterscheinung | 27. Juli 1973 |
| Maße | 23.5 cm x 15.5 cm |
| Gewicht | 201 Gramm |
| Format | Softcover |
| ISBN-13 | 9783540063889 |
| Seiten | 116 |
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