Ergodic Theorems for Group Actions: Informational and Thermodynamical Aspects

ISBN-13: 9780792317173 / Angielski / Twarda / 1992 / 399 str.

A. A. Tempel'man

Opis

One service mathematics has rendered the 'Et moi, ..., si j'avait Sil comment en revenir, je n'y serais point aIle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences_ Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science ..: 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Spis treści

Preface. Notations. Introduction. 1: Means and averageable functions. 2: Ergodicity and mixing. 3: Averaging sequences. Universal ergodic theorems. 4: Mean ergodic theorems. 5: Maximal and dominated ergodic theorems. 6. Pointwise ergodic theorems. 7. Ergodic theorems for homogeneous random measures. 8: Specific informational and thermodynamical characteristics of homogeneous random fields. Appendix. References. Index.