Titolo: The Metrical Theory of Jacobi-Perron Algorithm (Lecture Notes in Mathematics, 334)
Editore: Springer
Data di pubblicazione: 1973
Lingua: Inglese
ISBN 10: 3540063889
ISBN 13: 9783540063889
Rilegatura: Brossura
Condizione: New

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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.

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