Extensions of generic measure-preserving actions

Melleray, Julien

doi:10.5802/aif.2859

Cited by 6 publications

(6 citation statements)

References 17 publications

(32 reference statements)

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“…, we get (26) for any ξ ′ k -measurable set A. Since ξ ′ n → ε, by the diagonal process, we have a universal sequence g(n) and ( 25) implies (24).…”

Section: Let Us Modify Each Tmentioning

confidence: 97%

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On extensions of typical group actions

Ageev

2012

Preprint

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For every countable abelian group G we find the set of all its subgroups H (H ≤ G) such that a typical measure-preserving H-action on a standard atomless probability space (X, F , µ) can be extended to a free measure-preserving G-action on (X, F , µ). The description of all such pairs H ≤ G was made in purely group terms, in the language of the dual G, and G-actions with discrete spectrum. As an application, we answer a question when a typical H-action can be extended to a G-action with some dynamic property, or to a G-action at all. In particular, we offer first examples of pairs H ≤ G satisfying both G is countable abelian, and a typical H-action is not embeddable in a G-action.

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“…, we get (26) for any ξ ′ k -measurable set A. Since ξ ′ n → ε, by the diagonal process, we have a universal sequence g(n) and ( 25) implies (24).…”

Section: Let Us Modify Each Tmentioning

confidence: 97%

“…Recently Melleray proved Theorem 1.2 for H being finitely-generated via categorypreserving maps and a generalization of the classical Kuratowski-Ulam theorem (see [26]).…”

Section: Introductionmentioning

confidence: 99%

On extensions of typical group actions

Ageev

2012

Preprint

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“…Below, we focus on the first case only; the second case is handled by analogous methods. By the definition of µ y ⊗ µ z and since basic sets form a topological basis of C x , it is enough to show that (19) hῑ…”

Section: The Theorem On Koopman Representations and An Outline Of Its Proofmentioning

confidence: 99%

“…Unpacking further, we see that showing inequality (19) boils down to showing that, for each compact subset K of U with µ U,ῑ K > 0, there is some j ∈ N with µ j x (K) > 0. This translates into proving the following implication for each compact set K ⊆ U (20)…”

Section: The Theorem On Koopman Representations and An Outline Of Its Proofmentioning

confidence: 99%

Closed subgroups generated by generic measure automorphisms

Solecki¹

2013

Ergod. Th. Dynam. Sys.

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“…validated their experimental results of Raman analysis of pharmaceutical tablets along with the reflection of exiting photons back into the medium through RMC simulations. Photon propagation in breast tissue was simulated by Keller et al . to study the application of SORS in mastectomy to monitor the tumor margin.…”

Section: Introductionmentioning

confidence: 99%

Experimentally validated Raman Monte Carlo simulation for a cuboid object to obtain Raman spectroscopic signatures for hidden material

Periyasamy

Sil

Dhal

et al. 2015

J Raman Spectroscopy

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In conventional Raman spectroscopic measurements of liquids or surfaces the preferred geometry for detection of the Raman signal is the backscattering (or reflection) mode. For non‐transparent layered materials, sub‐surface Raman signals have been retrieved using spatially offset Raman spectroscopy (SORS), usually with light collection in the same plane as the point of excitation. However, as a result of multiple scattering in a turbid medium, Raman photons will be emitted in all directions. In this study, Monte Carlo simulations for a three‐dimensional layered sample with finite geometry have been performed to confirm the detectability of Raman signals at all angles and at all sides of the object. We considered a non‐transparent cuboid container (high density polyethylene) with explosive material (ammonium nitrate) inside. The simulation results were validated with experimental Raman intensities. Monte Carlo simulation results reveal that the ratio of sub‐surface to surface signals improves at geometries other than backscattering. In addition, we demonstrate through simulations the effects of the absorption and scattering coefficients of the layers, and that of the diameter of the excitation beam. The advantage of collecting light from all possible 4π angles, over other collection modes, is that this technique is not geometry specific and molecular identification of layers underneath non‐transparent surfaces can be obtained with minimal interference from the surface layer. To what extent all sides of the object will contribute to the total signal will depend on the absorption and scattering coefficients and the physical dimensions. Copyright © 2015 John Wiley & Sons, Ltd.

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Extensions of generic measure-preserving actions

Cited by 6 publications

References 17 publications

On extensions of typical group actions

On extensions of typical group actions

Closed subgroups generated by generic measure automorphisms

Experimentally validated Raman Monte Carlo simulation for a cuboid object to obtain Raman spectroscopic signatures for hidden material

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