The Metrical Theory of Jacobi-Perron Algorithm: 334 - Brossura

Schweiger, Fritz

 
9783540063889: The Metrical Theory of Jacobi-Perron Algorithm: 334

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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9780387063881: THE METRICAL THEORY OF JACOBI-PERRON ALGORITHM (LECTURE NOTES IN MATHEMATICS, 334)

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ISBN 10:  0387063889 ISBN 13:  9780387063881
Brossura