The Automorphism Group of the Gaussian Measure Cannot Act Pointwise

  title={The Automorphism Group of the Gaussian Measure Cannot Act Pointwise},
  author={B. TSIRELSON E. GLASNER and Benjamin Weiss},
Classical ergodic theory deals with measure (or measure class) preserving actions of locally compact groups on Lebesgue spaces. An important tool in this setting is a theorem of Mackey which provides spatial models for Boolean G-actions. We show that in full generality this theorem does not hold for actions of Polish groups. In particular there is no Borel model for the Polish automorphism group of a Gaussian measure. In fact, we show that this group as well as many other Polish groups do not… CONTINUE READING
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