F. Schweiger

The Metrical Theory of Jacobi-Perron Algorithm

• Broschiertes Buch

Produktbeschreibung

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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Produktdetails

• Lecture Notes in Mathematics 334
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-06388-9
• 1973.
• Seitenzahl: 124
• Erscheinungstermin: 27. Juli 1973
• Englisch
• Abmessung: 235mm x 155mm x 8mm
• Gewicht: 214g
• ISBN-13: 9783540063889
• ISBN-10: 3540063889
• Artikelnr.: 23380265

Inhaltsangabe

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.