IM PAN
INSTITUTE OF MATHEMATICS · POLISH ACADEMY OF SCIENCES
COLLOQUIUM
MATHEMATICUM
ISSN: 0010-1354(p) 1730-6302(e)
  
Absolutely continuous, invariant measures for dissipative, ergodic transformations
Jon Aaronson1, Tom Meyerovitch2
Colloq. Math. 110 (2008), 193-199
doi:10.4064/cm110-1-7

Abstract: 
We show that a dissipative, ergodic {measure preserving transformation} of a $\sigma $-finite, non-atomic measure space always has many non-proportional, absolutely continuous, invariant measures and is ergodic with respect to each one of these.

MSC (2000): 37A05, 37A40.
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  1. School of Mathematical Sciences
    Tel Aviv University
    69978 Tel Aviv, Israel
  2. School of Mathematical Sciences
    Tel Aviv University
    69978 Tel Aviv, Israel