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Shift invariant measures and simple spectrum

100%

Kłopotowski A., Nadkarni M. G.

Colloquium Mathematicum

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2000

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tom 84/85

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nr 2

385-394

EN

We consider some descriptive properties of supports of shift invariant measures on $ℂ^{ℤ}$ under the assumption that the closed linear span (in $L^{2}$) of the co-ordinate functions on $ℂ^{ℤ}$ is all of $L^{2}$.

2

Genericity of nonsingular transformations with infinite ergodic index

100%

Choksi J. R., Nadkarni M. G.

Colloquium Mathematicum

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2000

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tom 84/85

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nr 1

195-201

EN

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 $G_δ$ 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 measure. Exploring other possible (more restrictive) definitions of infinite ergodic index, we find, somewhat surprisingly, that if a nonsingular transformation on a Lebesgue probability space has an infinite} Cartesian power which is nonsingular with respect to the power measure, then it has to be measure preservingit.

3

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On sequences of σ-algebras

60%

Nadkarni M. G., Ramachandran D., Bhaskara-Rao K. P. S.

Colloquium Mathematicum

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1974-1975

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tom 32

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nr 2

219-226

Ograniczanie wyników

3 Colloquium Mathematicum

3 Nadkarni M. G.

1 Bhaskara-Rao K. P. S.

1 Choksi J. R.

1 Kłopotowski A.

1 Ramachandran D.

2 2000

1 1975

Shift invariant measures and simple spectrum

Genericity of nonsingular transformations with infinite ergodic index

On sequences of σ-algebras