The Experts below are selected from a list of 267 Experts worldwide ranked by ideXlab platform
Michel Théra - One of the best experts on this subject based on the ideXlab platform.
-
ekeland s inverse function Theorem in graded frechet spaces revisited for multifunctions
Journal of Mathematical Analysis and Applications, 2018Co-Authors: Van Ngai Huynh, Michel ThéraAbstract:Abstract In this paper, we present some inverse function Theorems and implicit function Theorems for set-valued mappings between Frechet spaces. The proof relies on Lebesgue's Dominated Convergence Theorem and on Ekeland's variational principle. An application to the existence of solutions of differential equations in Frechet spaces with non-smooth data is given.
-
Ekeland's inverse function Theorem in graded Fr{\'e}chet spaces revisited for multifunctions
arXiv: Classical Analysis and ODEs, 2016Co-Authors: Van Ngai Huynh, Michel ThéraAbstract:In this paper, we present some implicit function Theorems for set-valued mappings between Frechet spaces. The proof relies on Lebesgue's Dominated Convergence Theorem and on Ekeland's variational principle. An application to the existence of solutions of differential equations in Frechet spaces with non-smooth data is given.
-
ekeland s inverse function Theorem in graded fr e chet spaces revisited for multifunctions
arXiv: Classical Analysis and ODEs, 2016Co-Authors: Van Ngai Huynh, Michel ThéraAbstract:In this paper, we present some implicit function Theorems for set-valued mappings between Frechet spaces. The proof relies on Lebesgue's Dominated Convergence Theorem and on Ekeland's variational principle. An application to the existence of solutions of differential equations in Frechet spaces with non-smooth data is given.
Sergio A Pernice - One of the best experts on this subject based on the ideXlab platform.
-
divergence of perturbation theory steps towards a convergent series
Physical Review D, 1998Co-Authors: Gerardo Enrique Oleaga Apadula, Sergio A PerniceAbstract:The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of Lebesgue's Dominated Convergence Theorem using familiar techniques of quantum held theory. That Theorem governs the validity (or lack of it) of the formal manipulations done to generate the perturbative series in the functional integral formalism. The aspects of the perturbative series that need to be modified to obtain a convergent series are presented. Useful tools for a practical implementation of these modifications are developed. Some resummation methods are analyzed in the light of the above mentioned mechanism.
-
On the Mechanism Underlying the Divergence of Perturbation Theory
Functional Integration, 1997Co-Authors: Sergio A PerniceAbstract:It is well known that perturbation theory in quantum mechanics and quantum field theory generates a divergent series. It has been shown recently (hep-th/9609139) that such divergence can be understood in the context of Lebesgue’s Dominated Convergence Theorem. That Theorem governs the validity of the formal manipulation done to generate the perturbative series in the functional integral formalism. It was shown that one of its hypothesis is violated in theories like the λo4 theory in 1, 2 or 3 space-time dimensions. Question: given that in 4 dimensions a new source of divergence appears (renormalons), can they also be understood in the context of Lebesgue’s Theorem?
Qian-qian Zhou - One of the best experts on this subject based on the ideXlab platform.
-
Convergences of Random Variables under Sublinear Expectations
Chinese Annals of Mathematics Series B, 2018Co-Authors: Ze-chun Hu, Qian-qian ZhouAbstract:In this note, the authors survey the existing Convergence results for random variables under sublinear expectations, and prove some new results. Concretely, under the assumption that the sublinear expectation has the monotone continuity property, the authors prove that Convergence in capacity is stronger than Convergence in distribution, and give some equivalent characterizations of Convergence in distribution. In addition, they give a Dominated Convergence Theorem under sublinear expectations, which may have its own interest.
-
Convergences of Random Variables under Sublinear Expectations
arXiv: Probability, 2016Co-Authors: Ze-chun Hu, Qian-qian ZhouAbstract:In this note, we will survey the existing Convergence results for random variables under sublinear expectations, and prove some new results. Concretely, under the assumption that the sublinear expectation has the monotone continuity property, we will prove that $L^p$ Convergence is stronger than Convergence in capacity, Convergence in capacity is stronger than Convergence in distribution, and give some equivalent characterizations of Convergence in distribution. In addition, we give a Dominated Convergence Theorem under sublinear expectations, which may have its own interest.
Shoumei Li - One of the best experts on this subject based on the ideXlab platform.
-
NL-MUA - On Convergence Theorems of Set-Valued Choquet Integrals
Advances in Intelligent and Soft Computing, 2020Co-Authors: Hongxia Wang, Shoumei LiAbstract:The article aims at discussing the Choquet integrals of set-valued random variables with respect to capacities. We firstly state representation Theorems and subadditive property of set-valued Choquet integrals. Then we mainly prove Fatou’s Lemmas, Lesbesgue Dominated Convergence Theorem and monotone Convergence Theorems of set-valued Choquet integrals under the weaker conditions than that in previous works.
-
Some properties and Convergence Theorems of set-valued Choquet integrals
Fuzzy Sets and Systems, 2013Co-Authors: Hongxia Wang, Shoumei LiAbstract:The paper aims at discussing the set-valued Choquet integral, which is the integral of set-valued random variables with respect to capacities. We mainly present representation Theorems of the set-valued random variable by using a sequence of Choquet integrable selections and then we investigate some properties of set-valued Choquet integrals, especially subadditive property and inequality of the metric of set-valued Choquet integrals. We also prove Fatou's Lemmas, Lebesgue Dominated Convergence Theorem and monotone Convergence Theorem of set-valued Choquet integrals under the weaker conditions than that in previous works.
Jun Kawabe - One of the best experts on this subject based on the ideXlab platform.
-
MDAI - Convergence in Measure Theorems of the Choquet Integral Revisited.
Modeling Decisions for Artificial Intelligence, 2020Co-Authors: Jun KawabeAbstract:The validity of the monotone Convergence Theorem, the Fatou and the reverse Fatou lemmas, and the Dominated Convergence Theorem of the Choquet integral of measurable functions converging in measure are fully characterized by the conditional versions of the monotone autocontinuity and the autocontinuity. In those Theorems the nonadditive measure may be infinite and the functions may be unbounded. The dual measure forms and the extension to symmetric and asymmetric Choquet integrals are also discussed.
-
The Vitali Convergence in measure Theorem of nonlinear integrals
Fuzzy Sets and Systems, 2020Co-Authors: Jun KawabeAbstract:Abstract The Vitali Convergence in measure Theorem for the abstract Lebesgue integral is fundamental in Lebesgue integration theory and yields the bounded Convergence Theorem and the Dominated Convergence Theorem as its applications. In this paper, in a unified way using the perturbation method the Vitali Convergence in measure Theorem is established for nonlinear integrals such as the Choquet, Sipos, Sugeno, and Shilkret integrals, and their symmetric and asymmetric extensions. It is derived from the Fatou and the reverse Fatou type lemmas for perturbative nonlinear integral functionals.
-
The Choquet integral in Riesz space
Fuzzy Sets and Systems, 2008Co-Authors: Jun KawabeAbstract:A comprehensive discussion of the theory of Choquet integration in a Riesz space is given. In particular, it is proved that the monotone Convergence Theorem, the Fatou lemma, and the Dominated Convergence Theorem are still valid for Riesz space-valued non-additive measures if we assume that the Riesz space has a new property concerning the cardinality of the set of points of discontinuity of a monotone function.