---

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.

---

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.

---