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 70 libraries
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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