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.
Samuel Kotz, Narayanaswamy Balakrishnan, Norman L. Johnson, USA) Kotz, Samuel (George Washington University, Washington, DC, Canada) Balakrishnan, Narayanaswamy (McMaster University, USA) Johnson, Norman L. (University of North Carolina at Chapel Hill, NC, Norman L Johnson