The metrical theory of Jacobi-Perron algorithm
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Bibliographic Information
The metrical theory of Jacobi-Perron algorithm
(Lecture notes in mathematics, 334)
Springer-Verlag, 1973
- : Germany
- : U.S.
Available at / 69 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: GermanyL/N||LNM||3341979171
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science研究室
511.8/SCH972020805932
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Note
Bibliography: p. 106-111
Description and Table of Contents
Table of Contents
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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