The Metrical Theory of Jacobi-Perron Algorithm
Published on 27. July 1973
Book
Paperback/Softback
VIII, 116 pages
978-3-540-06388-9 (ISBN)
Description
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.
More details
Series
Edition
1973 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
VIII, 116 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 8 mm
Weight
201 gr
ISBN-13
978-3-540-06388-9 (9783540063889)
DOI
10.1007/BFb0059845
Schweitzer Classification
Content
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.