ISSN:
1432-2064
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We consider a Lebesgue measure space (M, ∇, m). By an automorphism of (M, ∇, m) we mean a bi-measurable transformation of (M, ∇, m) that together with its inverse is non-singular with respeot to m. We study an equivalence relation between these automorphisms that we call the weak equivalence. Two automorphisms S and T are weakly equivalent if there is an automorphism U such that for almost all xε M U maps the S-orbit of x onto the T-orbit of U x. Ergodicity, the existence of a finite invariant measure, the existenoe of a σ-finite infinite invariant measure, and the non-existence of such measures are invariants of weak equivalenoe. In this paper and in its sequel we solve the problem of weak equivalenoe for a class of automorphisms that comprises all ergodic automorphisms that admit a σ-finite invariant measure, and also certain ergodic automorphisms that do not admit such a measure.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00531811
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