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Summary We study the integration theory for general integral metrics when restricted to upper integrals q, finding improvements in the relation between the classes of the q-integrable and the ql-integrable functions. We give new results and notions which lead to the desirable characterizations of q-integrable functions as ql-integrable f with q(|f|) < ∞, and of ql-integrable functions via the integrability of their upper truncations, under natural conditions which are fulfilled in most
finitely additive integration theories. 相似文献
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利用对偶理论与可测集值映射理论等,本文首次证明了一般非线性随机规划问题最优值和最优解的可测性,从而为研究它们的概率分布、矩等分布问题以及一般随机规划问题的实际求解奠定了理论基础. 相似文献
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设T,X是完备可分的度量空间,T×X是乘积空间.设ν是T上的完备的Borel概率测度,τ是X上的预测度.从ν和τ出发,可以通过两种不同方式定义乘积空间T×X上的测度.证明在τ是σ-有限的情形下,这两种方式定义的测度都等于T×X上的乘积测度ν×τ*,其中τ*表示由τ按方法Ⅰ所构造的外测度;在τ是非σ-有限时,证明了在一定的条件下函数τ(Et)与τ*(Et)都是T上的可测函数,其中E T×X,Et={x∈X;(t,x)∈E}. 相似文献
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莫愿斌 《贵州大学学报(自然科学版)》2002,19(1):1-17
考虑非局部发展问题。首先对主算子为紧半群无穷小生成元,在较弱的假设条件下,证明温和解是存在的。同时研究主算子为解析半群时温和解的正则性问题,进而对主算子为解析紧半群问题给出一个有用的结果。最后,以一个例子展示理论结果的应用。 相似文献
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A quantum-mechanical theory of joint nonideal measurement of incompatible polarization observables is applied to an EPR-like experiment. It is demonstrated that this experiment yields both information satisfying and information violating the Bell inequalities. The measurement is also discussed in the context of a local hidden-variables theory. It is argued that the violation of an additional assumption of reproducibility of the hidden variable rather than violation of locality may be responsible for the violation of the Bell inequalities. 相似文献
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Germán A. Enciso Morris W. Hirsch Hal L. Smith 《Journal of Dynamics and Differential Equations》2008,20(1):115-132
Classical results in the theory of monotone semiflows give sufficient conditions for the generic solution to converge toward
an equilibrium or toward the set of equilibria (quasiconvergence). In this paper, we provide new formulations of these results
in terms of the measure-theoretic notion of prevalence, developed in Christensen (Israel J. Math., 13, 255–260, 1972) and Hunt et al. (Bull. Am. Math. Soc., 27, 217–238, 1992). For monotone reaction–diffusion systems with Neumann boundary conditions on convex domains, we show the
prevalence of the set of continuous initial conditions corresponding to solutions that converge to a spatially homogeneous
equilibrium. We also extend a previous generic convergence result to allow its use on Sobolev spaces. Careful attention is
given to the measurability of the various sets involved. 相似文献
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N. S. Papageorgiou 《Journal of Optimization Theory and Applications》1987,53(2):259-268
In the present paper, we generalize, within the family of convex-valued multifunctions, a selection theorem of Cole (Ref. 1). This then leads us to prove some new results concerning Cesari's property (Q) and to the introduction of the Cesari limit of sets, which is then compared to the Kuratowski-Mosco limit.This work was done while the author was a visiting professor at the University of Pavia, Pavia, Italy. Financial support was provided by CNR and by NSF Grant No. 84-03135. 相似文献
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阎国军 《郑州大学学报(理学版)》2001,33(1):7-9
利用测度论工具对随机过程进行深入的研究时,往往需要假设随机过程具有某种可测性.为了从另一个角度说明这个假设的必要性,构造一类不可测的但在任意时刻都以概率1为0的随机过程;并且利用空间联合的方法证明了任意有限维分布族都存在着分布族与之相同但不可测的随机过程. 相似文献