A class of ergodic transformations having simple spectrum

A class of ergodic, measure-preserving, invertible point transformations is defined, called class S. Any measurepreserving point transformation induces a unitary operator on the Hilbert space of ℒ2-functions. A theorem is proved here which implies that the operator induced by any transformation in class S has simple spectrum. [It is then a known result that the transformations in class S have zero entropy.].