Singular invariant measures on the line
V. Mandrekar, M. Nadkarni, D. Patil (1970)
Studia Mathematica
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Displaying similar documents to “Non singular transformations and spectral analysis of measures”
Singular invariant measures on the line
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Genericity of nonsingular transformations with infinite ergodic index
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It is shown that in the group of invertible measurable nonsingular transformations on a Lebesgue probability space, endowed with the coarse topology, the transformations with infinite ergodic index are generic; they actually form a dense set. (A transformation has infinite ergodic index if all its finite Cartesian powers are ergodic.) This answers a question asked by C. Silva. A similar result was proved by U. Sachdeva in 1971, for the group of transformations preserving an infinite...
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Conditions for the existence of measurable and integrable solutions of the cohomology equation on a measure space are deduced. They follow from the study of the ergodic structure corresponding to some families of bidimensional linear difference equations. Results valid for the non-measure-preserving case are also obtained
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