Transformations With Discrete Spectrum are Stacking Transformations

The stacking method (see [1] and [ 5 , Section 6 ]) has been used with great success in ergodic theory to construct a wide variety of examples of ergodic transformations (see, for example, [ 1 ; 3 ; 4 ; 5 ; 7 ]). However very little is known in general about the class of transformations which can be constructed by the stacking method using single stacks. In particular there is no simple characterization of the class .