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AuthorSchweiger, Fritz. author
TitleThe Metrical Theory of Jacobi-Perron Algorithm [electronic resource] / by Fritz Schweiger
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1973
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Descript VIII, 116 p. online resource


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

Mathematics Mathematics Mathematics general


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