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Elena R. Loubenets - One of the best experts on this subject based on the ideXlab platform.
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nonsignaling as the consistency condition for local quasi classical probability modeling of a general multipartite correlation scenario
Journal of Physics A, 2012Co-Authors: Elena R. LoubenetsAbstract:We specify for a general correlation scenario a particular type of local quasi hidden variable (LqHV) model (Loubenets 2012 J. Math. Phys. 53 022201)—a deterministic LqHV model, where all joint probability distributions of a correlation scenario are simulated via a single Measure space with a normalized bounded Real-Valued Measure not being necessarily positive and random variables, each depending only on a setting of the corresponding Measurement at the corresponding site. We prove that an arbitrary multipartite correlation scenario admits a deterministic LqHV model if and only if all its joint probability distributions satisfy the consistency condition, constituting the general nonsignaling condition formulated in Loubenets (2008 J. Phys. A: Math. Theor. 41 445303). This mathematical result specifies a new probability model that has a Measure-theoretic structure resembling the structure of the classical probability model but incorporates the latter only as a particular case. The local version of this quasi-classical probability model covers the probabilistic description of each nonsignaling correlation scenario, in particular, each correlation scenario on a multipartite quantum state.
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nonsignaling as the consistency condition for local quasi classical probability modelling of a general multipartite correlation scenario
arXiv: Quantum Physics, 2011Co-Authors: Elena R. LoubenetsAbstract:We specify for a general correlation scenario a particular type of a local quasi hidden variable (LqHV) model [J. Math. Phys. 53 (2012), 022201] -- a deterministic LqHV model, where all joint probability distributions of a correlation scenario are simulated via a single Measure space with a normalized bounded Real-Valued Measure not necessarily positive and random variables, each depending only on a setting of the corresponding Measurement at the corresponding site. We prove that an arbitrary multipartite correlation scenario admits a deterministic LqHV model if and only if all its joint probability distributions satisfy the consistency condition constituting the general nonsignaling condition formulated in [J. Phys. A: Math. Theor. 41 (2008), 445303]. This mathematical result specifies a new probability model that has the Measure-theoretic structure resembling the structure of the classical probability model but incorporates the latter only as a particular case. The local version of this quasi classical probability model covers the probabilistic description of every nonsignaling correlation scenario, in particular, each correlation scenario on an multipartite quantum state.
Carlo Bertoluzza - One of the best experts on this subject based on the ideXlab platform.
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a generalized Real Valued Measure of the inequality associated with a fuzzy random variable
International Journal of Approximate Reasoning, 2001Co-Authors: Carmen M Alonso, Teofilo Brezmes Brezmes, Asuncion M Lubiano, Carlo BertoluzzaAbstract:Abstract Fuzzy random variables have been introduced by Puri and Ralescu as an extension of random sets. In this paper, we first introduce a Real-Valued generalized Measure of the “relative variation” (or inequality) associated with a fuzzy random variable. This Measure is inspired in Csiszar's f-divergence, and extends to fuzzy random variables many well-known inequality indices. To guarantee certain relevant properties of this Measure, we have to distinguish two main families of Measures which will be characterized. Then, the fundamental properties are derived, and an outstanding Measure in each family is separately examined on the basis of an additive decomposition property and an additive decomposability one. Finally, two examples illustrate the application of the study in this paper.
Carmen M Alonso - One of the best experts on this subject based on the ideXlab platform.
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a generalized Real Valued Measure of the inequality associated with a fuzzy random variable
International Journal of Approximate Reasoning, 2001Co-Authors: Carmen M Alonso, Teofilo Brezmes Brezmes, Asuncion M Lubiano, Carlo BertoluzzaAbstract:Abstract Fuzzy random variables have been introduced by Puri and Ralescu as an extension of random sets. In this paper, we first introduce a Real-Valued generalized Measure of the “relative variation” (or inequality) associated with a fuzzy random variable. This Measure is inspired in Csiszar's f-divergence, and extends to fuzzy random variables many well-known inequality indices. To guarantee certain relevant properties of this Measure, we have to distinguish two main families of Measures which will be characterized. Then, the fundamental properties are derived, and an outstanding Measure in each family is separately examined on the basis of an additive decomposition property and an additive decomposability one. Finally, two examples illustrate the application of the study in this paper.
Emanuele Bottazzi - One of the best experts on this subject based on the ideXlab platform.
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a Real Valued Measure on non archimedean field extensions of mathbb r
arXiv: Functional Analysis, 2020Co-Authors: Emanuele BottazziAbstract:We introduce a Real-Valued Measure ${m_L}$ on non-Archimedean ordered fields $(\mathbb{F},<)$ that extend the field of Real numbers $(\mathbb{R},<)$. The definition of ${m_L}$ is inspired by the Loeb Measures of hyperReal fields in the framework of Robinson's analysis with infinitesimals. The Real-Valued Measure ${m_L}$ turns out to be general enough to obtain a canonical measurable representative in $\mathbb{F}$ for every Lebesgue measurable subset of $\mathbb{R}$, moreover, the Measure of the two sets is equal. In addition, $m_L$ it is more expressive than a class of non-Archimedean uniform Measures. We focus on the properties of the Real-Valued Measure in the case where $\mathbb{F}=\mathcal{R}$, the Levi-Civita field. In particular, we compare ${m_L}$ with the uniform non-Archimedean Measure over $\mathcal{R}$ developed by Shamseddine and Berz, and we prove that the first is infinitesimally close to the second, whenever the latter is defined. We also define a Real-Valued integral for functions on the Levi-Civita field, and we prove that every Real continuous function has an integrable representative in $\mathcal{R}$. Recall that this result is false for the current non-Archimedean integration over $\mathcal{R}$. The paper concludes with a discussion on the representation of the Dirac distribution by pointwise functions on non-Archimedean domains.
Bottazzi Emanuele - One of the best experts on this subject based on the ideXlab platform.
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A Real-Valued Measure on non-Archimedean field extensions of $\mathbb{R}$
2020Co-Authors: Bottazzi EmanueleAbstract:We introduce a Real-Valued Measure ${m_L}$ on non-Archimedean ordered fields $(\mathbb{F},
