عنوان

Linear fractional transformations mod one and ergodic theory

TLets623122

Linear fractional transformations mod one and ergodic theory

[Thesis]

Rudolpher, Stephan Martin

University of London

1968

Thesis (Ph.D.)

1968

After an introductory chapter, we study characterisations of mixing, weak mixing and ergodicity of a finite measure-preserving transformation T due to N. Oishi [25]. These characterisations are in terms of convergence of suitably defined entropies of finite partitions. We show that the characterisations can be given in terms of (countable) partitions with finite entropy, extend the characterisation to mixing of degree r and give further characterisations in terms of convergence of the suitably defined measures of Jordan measurable sets and, in the case of a compact measure space, in terms of weak convergence of these measures. It is shown that these characterisations cannot be extended to convergence of the corresponding entropies of TxT nor to all measurable subsets, respectively.

Rudolpher, Stephan Martin

Imperial College London

p

[Thesis]

276903

a

Y