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The Metrical Theory of Jacobi-Perron Algorithm de F. Schweiger

The Metrical Theory of Jacobi-Perron Algorithm: Lecture Notes in Mathematics, cartea 334

Autor F. Schweiger
en Limba Engleză Paperback – 27 iul 1973

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Specificații

ISBN-13: 9783540063889
ISBN-10: 3540063889
Pagini: 124
Ilustrații: VIII, 116 p.
Dimensiuni: 155 x 235 x 7 mm
Greutate: 0.19 kg
Ediția:1973
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Lecture Notes in Mathematics

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

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.