The Experts below are selected from a list of 246 Experts worldwide ranked by ideXlab platform
Congxin Wu - One of the best experts on this subject based on the ideXlab platform.
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Radon–Nikodym Theorem and Vitali–Hahn–Saks Theorem on fuzzy number measures in Banach spacers
Fuzzy Sets and Systems, 2001Co-Authors: Jianrong Wu, Congxin WuAbstract:Abstract Radon–Nikodym Theorem is established on fuzzy number measures in Banach spaces, Vitali–Hahn–Saks Theorem is generalized to set valued measures and fuzzy number measures.
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radon nikodym Theorem and vitali hahn saks Theorem on fuzzy number measures in banach spacers
Fuzzy Sets and Systems, 2001Co-Authors: Jianrong Wu, Congxin WuAbstract:Abstract Radon–Nikodym Theorem is established on fuzzy number measures in Banach spaces, Vitali–Hahn–Saks Theorem is generalized to set valued measures and fuzzy number measures.
Jianrong Wu - One of the best experts on this subject based on the ideXlab platform.
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Radon–Nikodym Theorem and Vitali–Hahn–Saks Theorem on fuzzy number measures in Banach spacers
Fuzzy Sets and Systems, 2001Co-Authors: Jianrong Wu, Congxin WuAbstract:Abstract Radon–Nikodym Theorem is established on fuzzy number measures in Banach spaces, Vitali–Hahn–Saks Theorem is generalized to set valued measures and fuzzy number measures.
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radon nikodym Theorem and vitali hahn saks Theorem on fuzzy number measures in banach spacers
Fuzzy Sets and Systems, 2001Co-Authors: Jianrong Wu, Congxin WuAbstract:Abstract Radon–Nikodym Theorem is established on fuzzy number measures in Banach spaces, Vitali–Hahn–Saks Theorem is generalized to set valued measures and fuzzy number measures.
Paul Poncet - One of the best experts on this subject based on the ideXlab platform.
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The idempotent Radon--Nikodym Theorem has a converse statement
Information Sciences, 2014Co-Authors: Paul PoncetAbstract:Idempotent integration is an analogue of the Lebesgue integration where $\sigma$-additive measures are replaced by $\sigma$-maxitive measures. It has proved useful in many areas of mathematics such as fuzzy set theory, optimization, idempotent analysis, large deviation theory, or extreme value theory. Existence of Radon--Nikodym derivatives, which turns out to be crucial in all of these applications, was proved by Sugeno and Murofushi. Here we show a converse statement to this idempotent version of the Radon--Nikodym Theorem, i.e. we characterize the $\sigma$-maxitive measures that have the Radon--Nikodym property.
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The idempotent Radon–Nikodym Theorem has a converse statement
Information Sciences, 2014Co-Authors: Paul PoncetAbstract:Idempotent integration is an analogue of the Lebesgue integration where $\sigma$-additive measures are replaced by $\sigma$-maxitive measures. It has proved useful in many areas of mathematics such as fuzzy set theory, optimization, idempotent analysis, large deviation theory, or extreme value theory. Existence of Radon--Nikodym derivatives, which turns out to be crucial in all of these applications, was proved by Sugeno and Murofushi. Here we show a converse statement to this idempotent version of the Radon--Nikodym Theorem, i.e. we characterize the $\sigma$-maxitive measures that have the Radon--Nikodym property.
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What is the role of continuity in continuous linear forms representation
arXiv: General Topology, 2010Co-Authors: Paul PoncetAbstract:The recent extensions of domain theory have proved particularly efficient to study lattice-valued maxitive measures, when the target lattice is continuous. Maxitive measures are defined analogously to classical measures with the supremum operation in place of the addition. Building further on the links between domain theory and idempotent analysis highlighted by Lawson (2004), we investigate the concept of domain-valued linear forms on an idempotent (semi)module. In addition to proving representation Theorems for continuous linear forms, we address two applications: the idempotent Radon--Nikodym Theorem and the idempotent Riesz representation Theorem. To unify similar results from different mathematical areas, our analysis is carried out in the general Z framework of domain theory.
Christopher D. Edgar - One of the best experts on this subject based on the ideXlab platform.
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A Development of Continuous-Time Transfer Entropy.
arXiv: Probability, 2019Co-Authors: Joshua Cooper, Christopher D. EdgarAbstract:Transfer entropy (TE) was introduced by Schreiber in 2000 as a measurement of the predictive capacity of one stochastic process with respect to another. Originally stated for discrete time processes, we expand the theory in line with recent work of Spinney, Prokopenko, and Lizier to define TE for stochastic processes indexed over a compact interval taking values in a Polish state space. We provide a definition for continuous time TE using the Radon-Nikodym Theorem, random measures, and projective limits of probability spaces. As our main result, we provide necessary and sufficient conditions to obtain this definition as a limit of discrete time TE, as well as illustrate its application via an example involving Poisson point processes. As a derivative of continuous time TE, we also define the transfer entropy rate between two processes and show that (under mild assumptions) their stationarity implies a constant rate. We also investigate TE between homogeneous Markov jump processes and discuss some open problems and possible future directions.
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Transfer Entropy in Continuous Time.
arXiv: Probability, 2019Co-Authors: Joshua Cooper, Christopher D. EdgarAbstract:Transfer entropy (TE) was introduced by Schreiber in 2000 as a measurement of the predictive capacity of one stochastic process with respect to another. Originally stated for discrete time processes, we expand the theory of TE to stochastic processes indexed over a compact interval taking values in a Polish state space. We provide a definition for continuous time TE using the Radon-Nikodym Theorem, random measures, and projective limits of probability spaces. Furthermore, we provide necessary and sufficient conditions to obtain this definition as a limit of discrete time TE, as well as illustrate its application via an example involving Poisson point processes. As a derivative of continuous time TE, we also define the transfer entropy rate between two processes and show that (under mild assumptions) their stationarity implies a constant rate. We also investigate TE between homogeneous Markov jump processes and discuss some open problems and possible future directions.
Domenico Candeloro - One of the best experts on this subject based on the ideXlab platform.
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Atomicity related to non-additive integrability
Rendiconti del Circolo Matematico di Palermo (1952 -), 2016Co-Authors: Domenico Candeloro, Anca Croitoru, Alina Gavrilut, Anna Rita SambuciniAbstract:In this paper we present some results concerning Gould integrability of vector functions with respect to a monotone measure on finitely purely atomic measure spaces. As an application a Radon-Nikodym Theorem in this setting is obtained.
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A multivalued version of the Radon-Nikodym Theorem, via the single-valued Gould integral
arXiv: Functional Analysis, 2015Co-Authors: Domenico Candeloro, Anca Croitoru, Alina Gavrilut, Anna Rita SambuciniAbstract:Some topics concerning the Gould integral are presented here: new results of integrability on finite measure spaces with values in an M-space are given, together with a Radon-Nikodym Theorem relative to a Gould-type integral of real functions with respect to a multisubmeasure.
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Radon Nikodym Theorem for a pair of multisubmeasures with respect to the Gould integrability
arXiv: Functional Analysis, 2015Co-Authors: Domenico Candeloro, Anca Croitoru, Alina Gavrilut, Anna Rita SambuciniAbstract:Some topics concerning the Gould integral are presented here: new results of integrability on finite measure spaces with values in an M-space are given, together with a Radon-Nikodym Theorem relative to a Gould-type integral of real functions with respect to a multisubmeasure.
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Stochastic processes in nuclear spaces: quasi-martingales and decompositions
Mathematica Slovaca, 2005Co-Authors: James K. Brooks, Domenico Candeloro, Anna MartellottiAbstract:We prove a Radon-Nikodym Theorem for measures ranging in a special class of locally convex vector spaces, and deduce from it several decompositions for quasi martingales taking values in the same class of spaces.
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Handbook of Measure Theory - CHAPTER 6 – Radon-Nikodým Theorems
Handbook of Measure Theory, 2002Co-Authors: Domenico Candeloro, Aljoša VolčičAbstract:This chapter describes the various aspects of Radon–Nikodym Theorems. A general Radon–Nikodym Theorem for nonnegative finitely additive scalar measures is presented in the chapter from which the basic ideas of further results can be drawn. The conditions that permit even unbounded measures to have Radon–Nikodym derivatives are examined in the chapter. The results concerning Banach spaces possessing the so-called “Radon–Nikodym Property” (RNP) are presented in the chapter. The geometric concepts become essential tools for describing Banach spaces. The finitely additive measures taking values in Banach spaces and to the research of weaker types of derivatives are elaborated in the chapter. To find a characterization of the Radon–Nikodym property, the concept of completeness is required. A complex measure or function can be studied investigating separately its real and imaginary parts. It is proved in the chapter that convergence in measure implies convergence for some subsequence; hence, a strongly measurable function is essentially valuedseparably. It is found that the problems concerning the existence of a Radon–Nikodym derivative are harder when one allows also finitely additive measures into consideration. Some results concerning Radon–Nikodym derivatives for Sugeno integral are also presented in the chapter.
