Transformations which leave a measure quasi-invariant

V. Ya. Golodets

Institute of Low-Temperature Physics and Technology, Academy of Sciences of the Ukranian SSR

Abstract: It is shown that every countable group $G$ has a faithful representation as an ergodic freely-acting group of transformations of a commutative Neumann algebra $M$ with measure $\mu$, leaving the measure $\mu$ quasi-invariant, while there does not exist a measure $\mu'$ which is equivalent to $\mu$ and invariant with respect to $G$.

UDC: 513.78

Received: 08.10.1968

 English version: Mathematical Notes, 1970, 7:2, 134–136

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