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Weak Continuity of Riemann Integrable Functions in Lebesgue-Bochner Spaces 被引量:1
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作者 J.M.CALABUIG J.RODRíGUEZ E.A.SNCHEZ-PREZ 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2010年第2期241-248,共8页
In general, Banach space-valued Riemann integrable functions defined on [0, 1] (equipped with the Lebesgue measure) need not be weakly continuous almost everywhere. A Banach space is said to have the weak Lebesgue p... In general, Banach space-valued Riemann integrable functions defined on [0, 1] (equipped with the Lebesgue measure) need not be weakly continuous almost everywhere. A Banach space is said to have the weak Lebesgue property if every Riemann integrable function taking values in it is weakly continuous almost everywhere. In this paper we discuss this property for the Banach space LX^1 of all Bochner integrable functions from [0, 1] to the Banach space X. We show that LX^1 has the weak Lebesgue property whenever X has the Radon-Nikodym property and X* is separable. This generalizes the result by Chonghu Wang and Kang Wan [Rocky Mountain J. Math., 31(2), 697-703 (2001)] that L^1[0, 1] has the weak Lebesgue property. 展开更多
关键词 riemann integral Bochner integral Lebesgue-Bochner space weak Lebesgue property
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STABLE SUB-GAUSSIAN MODELS CONSTRUCTED BY POISSON PROCESSES 被引量:1
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作者 戴洪帅 李育强 《Acta Mathematica Scientia》 SCIE CSCD 2011年第5期1945-1958,共14页
In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend t... In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend this result to the two-parameter processes. At last, we consider the approximation of the subordinated fractional Brownian motion. 展开更多
关键词 stable sub-Gaussian process weak convergence Poisson process riemann integral
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