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CONVERGENCE THEOREMS AND MAXIMAL INEQUALITIES FOR MARTINGALE ergodic PROCESSES

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Acta Mathematica Scientia 2010年第4期30卷 1269-1279页

作者：罗光洲马璇刘培德 School of Mathematics and Statistics Hubei Normal University College of Sciences Huazhong Agricultural University School of Mathematics and Statistics Wuhan University

In this article, we study two types of martingale ergodic processes. We prove that a.e. convergence and L^p convergence as well as maximal inequalities, which are established both in ergodic theory and martingale setting, also hold well for these new sequences of random variables. Moreover, the corresponding theorems in the former two areas turn out to be degenerate cases of the martingale ergodic theorems proved here.

关键词： ergodic theory martingale convergence maximal inequalities

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CALCULUS ON CANTOR TRIADIC SET (I)-DERIVATIVE

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Applied Mathematics(A Journal of Chinese Universities) 1997年第4期12卷 483-492页

作者： XI LIFENG Department of Mathematics Zhejiang University Hangzhou

For real valued functions defined on Cantor triadic set, a derivative with corresponding formula of Newton Leibniz’s type is given. In particular, for the self similar functions and alternately jumping functions defined in this paper, their derivative and exceptional sets are studied accurately by using ergodic theory on Σ 2 and Duffin Schaeffer’s theorem concerning metric diophantine approximation. In addition, Haar basis of L 2(Σ 2) is constructed and Haar expansion of standard self similar function is given.

关键词： Fractal derivative on Cantor set exceptional set ergodic theory Duffin Schaeffer’ s theorem

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ergodic approach in studying a dynamical system

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Progress in Natural Science:Materials International 1995年第6期 10-19页

作者：周作领 China Guangzhou 510275 Lingnan College Zhongshan University

The development of dynamical systems bears a close relation to the ergodic theo-ry. The former discusses a continuous or differentiable action of a group on a topological space and the latter discusses the measure-pre... 详细信息

关键词： dynamical system ergodic theory entropy chaos.

Coverage control of multi-agent systems for ergodic exploration

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Coverage control of multi-agent systems for ergodic explorat...