The Metrical Theory of Jacobi-Perron Algorithm

F. Schweiger

ISBN 10: 3540063889 / ISBN 13: 9783540063889

Editore: Springer, Springer Berlin Heidelberg Jul 1973, 1973

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This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 124 pp. Englisch.

Codice articolo 9783540063889

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• Titolo: The Metrical Theory of Jacobi-Perron Algorithm
• Editore: Springer, Springer Berlin Heidelberg Jul 1973
• Data di pubblicazione: 1973
• Lingua: Inglese
• ISBN 10: 3540063889
• ISBN 13: 9783540063889
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 8 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 8 millimetri di profondità
• Peso: 201 grammi

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Contenuti

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.