Markov processes without a finite invariant measure

Spring 1975 at the Technological University of Eindhoven a group of people studied the chapter on finite invariant measures in Foguel's book on the ergodic theory of Markov processes [3]. This memorandum is a summary of the discussed topics, and it contains known results, or slight extensions of known results of which we were not able to discover them in literature. The material is divided in two parts. The first part deals with properties of Markov operators which do not admit a finite invariant measure, and the second part gives some applications to the theory of measurable transformations. The author is very much indebted to the members of the group: L. Groenewegen, K. van Hee, K van Harn, A. Nijst, D. Overdijk, B. Schaaf and F. Steutel. Without the stimulating discussions these notes would not have been written.