Postprint version. Published in Lecture Notes in Mathematics, Volume 1514, March 1, 1992, pages 114-123. Copyright © 1992 Springer. The original publication is available at http://dx.doi.org/ 10.1007/BFb0097531.
NOTE: At the time of publication, the author Theodore P. Hill was not yet affiliated with Cal Poly.
Measure preserving transformations generate stationary processes and vice versa. Which processes (X i ) correspond to the class of generalized measure preserving trans-formations? We give necessary conditions and show that they are sufficient for 2-valued processes as far as the marginals of (X0, X1, X2, X3) are concerned. The general problem remains open. Our main tool is a construction of a class of generalized measure preserving transformations which may be of independent interest.