The Experts below are selected from a list of 204 Experts worldwide ranked by ideXlab platform
Radko Mesiar - One of the best experts on this subject based on the ideXlab platform.
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Generalized convergence Theorems for monotone measures
Fuzzy Sets and Systems, 1Co-Authors: Yao Ouyang, Radko MesiarAbstract:Abstract In this paper, we propose three types of absolute continuity for monotone measures and present some of their basic properties. By means of these three types of absolute continuity, we establish generalized Egoroff's Theorem, generalized Riesz's Theorem and generalized Lebesgue's Theorem in the framework involving the ordered pair of monotone measures. The Egoroff Theorem, the Riesz Theorem and the Lebesgue Theorem in the traditional sense concerning a unique monotone measure are extended to the general case. These three generalized convergence Theorems include as special cases several previous versions of Egoroff-like Theorem, Riesz-like Theorem and Lebesgue-like Theorem for monotone measures, respectively.
Yao Ouyang - One of the best experts on this subject based on the ideXlab platform.
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Generalized convergence Theorems for monotone measures
Fuzzy Sets and Systems, 1Co-Authors: Yao Ouyang, Radko MesiarAbstract:Abstract In this paper, we propose three types of absolute continuity for monotone measures and present some of their basic properties. By means of these three types of absolute continuity, we establish generalized Egoroff's Theorem, generalized Riesz's Theorem and generalized Lebesgue's Theorem in the framework involving the ordered pair of monotone measures. The Egoroff Theorem, the Riesz Theorem and the Lebesgue Theorem in the traditional sense concerning a unique monotone measure are extended to the general case. These three generalized convergence Theorems include as special cases several previous versions of Egoroff-like Theorem, Riesz-like Theorem and Lebesgue-like Theorem for monotone measures, respectively.
Jun Li - One of the best experts on this subject based on the ideXlab platform.
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Lebesgue Theorems in non additive measure theory
Fuzzy Sets and Systems, 2005Co-Authors: Jinjie Song, Jun LiAbstract:In this paper, the sufficient and necessary conditions for different kinds of Lebesgue Theorem in non-additive measure theory are presented, respectively. The equivalence among the Lebesgue Theorem, the Monotone convergence Theorems of fuzzy and of Choquet integral are shown. As direct results of the Lebesgue Theorems, the necessary conditions for Egoroff's Theorem are given.
Maurice H. P. M. Van Putten - One of the best experts on this subject based on the ideXlab platform.
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A Riemann Sum Upper Bound in the Riemann--Lebesgue Theorem
SIAM Review, 1998Co-Authors: Maurice H. P. M. Van PuttenAbstract:The Riemann--Lebesgue Theorem is commonly proved in a few strokes using the theory of Lebesgue integration. Here, the upper bound $2\pi|c_k(f)|\le S_k(f)-s_k(f)$ for the Fourier coefficients ck is proved in terms of majoring and minoring Riemann sums Sk(f) and sf(k), respectively, for Riemann integrable functions f(x). This proof has been used in a course on methods of applied mathematics.
Tao Qian - One of the best experts on this subject based on the ideXlab platform.
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Clifford algebra approach to pointwise convergence of Fourier series on spheres
Science in China Series A: Mathematics, 2006Co-Authors: Minggang Fei, Tao QianAbstract:We offer an approach by means of Clifford algebra to convergence of Fourier series on unit spheres of even-dimensional Euclidean spaces. It is based on generalizations of Fueter's Theorem inducing quaternionic regular functions from holomorphic functions in the complex plane. We, especially, do not rely on the heavy use of special functions. Analogous Riemann-Lebesgue Theorem, localization principle and a Dini's type pointwise convergence Theorem are proved.
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Pointwise Convergence of Fourier Series on the Unit Sphere of R4 with the Quaternionic Setting
Advances in Analysis and Geometry, 2004Co-Authors: Shuang Liu, Tao QianAbstract:We offer a new approach to convergence of Fourier series on the unit sphere of the four-dimensional Euclidean space. The approach is via the quaternionic analysis setting with a crucial application of Fueter’s Theorem. Analogs to the Riemann-Lebesgue Theorem, localization principle and a Dini’s type pointwise convergence Theorem are proved.