The Metrical Theory of Jacobi-Perron Algorithm

Basic definitions....Pages 1-8
Cylinders....Pages 8-15
Increasing σ-fields....Pages 15-17
Conditional expectations....Pages 17-21
Ergodicity of the transformation....Pages 22-23
Existence of an equivalent invariant measure....Pages 23-28
The ergodic theorem....Pages 28-34
Kuzmin\'s Theorem....Pages 34-42
Convergence results....Pages 42-49
The Borel-Cantelli lemma of Schmidt-Philipp....Pages 49-54
Some extensions of Kuzmin\'s theorem....Pages 54-56
Outer measures....Pages 56-60
Hausdorff measures....Pages 60-63
Hausdorff dimension....Pages 63-65
Billingsley dimension....Pages 65-68
Comparison theorems....Pages 68-75
The main theorem of dimension theory of Jacobi algorithm....Pages 75-90
Ergodic invariant measures....Pages 90-94
Volume as approximation measure....Pages 94-98
Proof of the conjecture for n=1 and n=2....Pages 99-104
The metrical theory of Jacobi-Perron algorithm....Pages 105-105
Errata....Pages e1-e1