The Metrical Theory of Jacobi-Perron Algorithm
Schweiger, Fritz.
The Metrical Theory of Jacobi-Perron Algorithm [electronic resource] / by Fritz Schweiger. - VIII, 116 p. online resource. - Lecture Notes in Mathematics, 334 0075-8434 ; . - Lecture Notes in Mathematics, 334 .
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.
9783540470106
10.1007/BFb0059845 doi
Mathematics.
Mathematics, general.
QA1-939
510
The Metrical Theory of Jacobi-Perron Algorithm [electronic resource] / by Fritz Schweiger. - VIII, 116 p. online resource. - Lecture Notes in Mathematics, 334 0075-8434 ; . - Lecture Notes in Mathematics, 334 .
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.
9783540470106
10.1007/BFb0059845 doi
Mathematics.
Mathematics, general.
QA1-939
510