The Metrical Theory of Jacobi-Perron Algorithm

von F. Schweiger

124 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Reihe: Lecture Notes in Mathematics
• Themen: Mathematik und Naturwissenschaften Mathematik
• ISBN: 9783540063889
• Sprache: Englisch
• Erscheinungsdatum: 27.07.1973
• Größe: 235 x 155 mm
• Verlag: Springer