共查询到20条相似文献,搜索用时 31 毫秒
1.
Kenneth L. Kuttler 《Applicable analysis》2013,92(12):2456-2477
A method for obtaining measurable solutions to stochastic evolution equations in which there is no uniqueness for the corresponding non-stochastic equation is presented. It involves a technique based on a measurable selection theorem for set-valued functions. No assumptions are needed on the underlying probability space. An application is given to the stochastic Navier–Stokes problem in arbitrary dimensions. We also show the existence of measurable solutions to stochastic ordinary differential equations in which there is no uniqueness. A finite-dimensional generalization is given to adapted solutions in the case of a normal filtration and path uniqueness. 相似文献
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In this paper, we mainly discuss the measurable functional spaces based on strict pseudo-additions. Particularly, we obtained the some important theorems for the measurable functional spaces based on a strict pseudo-addition. Furthermore, we got that the some properties of the sequence of a.e. convergence and convergence in $\oplus$-measure, and the relationship between a.e. convergence and convergence in $\oplus$-measure on the measurable functional spaces based on a strict pseudo-addition. 相似文献
4.
In this note a note and simple technique is presented to replace the complicated one in [1] to obtain Hölder continuity of the weak solutions for a class of nonlinear parabolic equations with measurable coefficients, whose prototype is the singular p-Laplacian. This new approach is also applied to two other classes of nonlinear parabolic equations with measurable coefficients, whose weak solutions exhibit the similar property to those of equations mentioned above. 相似文献
5.
Shaoyi Zhang 《中国科学A辑(英文版)》1999,42(1):58-67
The existence theorem of the optimal measurable coupling of two probability kernels on a complete separable metric measurable
space is proved. Then by this theorem, a general ergodicity theorem for Markov processes is obtained. And as an immediate
application to particle systems the uniqueness theorem of the stationary distribution is supplemented, i.e. the uniqueness
theorem also implies the existence of the stationary distribution. 相似文献
6.
AbstractWe consider random set-valued measures with values in a separable Banach space. We prove two integral representation theorems using measurable multifunctions and set-valued integrals. The first theorem is valid for all separable Banach spaces, while the second holds for reflexive separable Banach spaces. 相似文献
7.
We consider how to represent the measurable sets in an infinite measure space. We use sequences of simple measurable sets converging under metrics to represent general measurable sets. Then we study the computability of the measure and the set operators of measurable sets with respect to such representations. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
8.
Alžbeta Michalíková 《Mathematica Slovaca》2008,58(1):63-76
In this paper an outer measure on IF-sets is studied as a mapping to the set of all compact subintervals of the unit interval.
We characterize the properties of the outer measure by the help of the properties of functions given by the edges of the intervals.
Then there are defined measurable elements and there is proved that the family of measurable elements is a lattice. Finally
the outer measure induced by a measure is constructed.
This paper was supported by Grant VEGA 1/2002/05. 相似文献
9.
A. G. Chentsov 《Russian Mathematics (Iz VUZ)》2008,52(3):58-68
We consider an attainability problem in a complete metric space on values of an objective operator h. We assume that the latter admits a uniform approximation by mappings which are tier with respect to a given measurable space with an algebra of sets. Let asymptotic-type constraints be defined as a nonempty family of sets in this measurable space. We treat ultrafilters of the measurable space as generalized elements; we equip this space of ultrafilters with a topology of a zero-dimensional compact (the Stone representation space). On this base we construct a correct extension of the initial problem, realizing the set of attraction in the form of a continuous image of the compact of feasible generalized elements. Generalizing the objective operator, we use the limit with respect to ultrafilters of the measurable space. This provides the continuity of the generalized version of h understood as a mapping of the zero-dimensional compact into the topological space metrizable with a total metric. 相似文献
10.
Alkhutov,Manedov在[1]中讨论了具有可测系数的线性一致抛物型方程的Dirichlet问题,其中系数满足:这里k0,k1,p(>n 2)是非负常数,本文讨论带有可测系数的一般线性一致抛物型方程的初-斜微商边值问题. 相似文献
11.
转移概率最优可测耦合的存在性 总被引:4,自引:1,他引:4
转移概率最优可测耦合的存在性是耦合理论中的基本问题之一,本文运用随机线性规划和s空间中的技巧,在较一般的条件下,给出转移概率最优可测耦合存在性的构造性证明. 相似文献
12.
Jason A. Schanker 《Mathematical Logic Quarterly》2011,57(3):266-280
In this article, we introduce the notion of weakly measurable cardinal, a new large cardinal concept obtained by weakening the familiar concept of a measurable cardinal. Specifically, a cardinal κ is weakly measurable if for any collection $\mathcal {A}$ containing at most κ+ many subsets of κ, there exists a nonprincipal κ‐complete filter on κ measuring all sets in $\mathcal {A}$. Every measurable cardinal is weakly measurable, but a weakly measurable cardinal need not be measurable. Moreover, while the GCH cannot fail first at a measurable cardinal, I will show that it can fail first at a weakly measurable cardinal. More generally, if κ is measurable, then we can make its weak measurability indestructible by the forcing Add(κ, η) for any η while forcing the GCH to hold below κ. Nevertheless, I shall prove that weakly measurable cardinals and measurable cardinals are equiconsistent. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
13.
Let M be a type I von Neumann algebra with the center Z and let LS(M) be the algebra of all locally measurable operators affiliated with M. We prove that every Z-linear derivation on LS(M) is inner. In particular, all Z-linear derivations on the algebras of measurable and respectively totally measurable operators are spatial and implemented
by elements of LS(M).
The text was submitted by the authors in English. 相似文献
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15.
Tomá s Domí nguez Benavides Genaro Ló pez Acedo Hong-Kun Xu 《Proceedings of the American Mathematical Society》1996,124(3):831-838
Some random fixed point theorems for set-valued operators are obtained. The measurability of certain marginal maps is also studied. The underlying measurable space is not assumed to be a Suslin family.
16.
D. Azagra J.B. Seoane-Sepúlveda 《Journal of Mathematical Analysis and Applications》2009,354(1):229-233
If f is continuous on the interval [a,b], g is Riemann integrable (resp. Lebesgue measurable) on the interval [α,β] and g([α,β])⊂[a,b], then f○g is Riemann integrable (resp. measurable) on [α,β]. A well-known fact, on the other hand, states that f○g might not be Riemann integrable (resp. measurable) when f is Riemann integrable (resp. measurable) and g is continuous. If c stands for the continuum, in this paper we construct a c2-dimensional space V and a c-dimensional space W of, respectively, Riemann integrable functions and continuous functions such that, for every f∈V?{0} and g∈W?{0}, f○g is not Riemann integrable, showing that nice properties (such as continuity or Riemann integrability) can be lost, in a linear fashion, via the composite function. Similarly we construct a c-dimensional space W of continuous functions such that for every g∈W?{0} there exists a c-dimensional space V of measurable functions such that f○g is not measurable for all f∈V?{0}. 相似文献
17.
We show that, if an MCP (monotonically countably paracompact) space fails to be collectionwise Hausdorff, then there is a measurable cardinal and that, if there are two measurable cardinals, then there is an MCP space that fails to be collectionwise Hausdorff.
18.
Vasco Brattka 《Mathematical Logic Quarterly》2005,51(1):19-44
The investigation of computational properties of discontinuous functions is an important concern in computable analysis. One method to deal with this subject is to consider effective variants of Borel measurable functions. We introduce such a notion of Borel computability for single‐valued as well as for multi‐valued functions by a direct effectivization of the classical definition. On Baire space the finite levels of the resulting hierarchy of functions can be characterized using a notion of reducibility for functions and corresponding complete functions. We use this classification and an effective version of a Selection Theorem of Bhattacharya‐Srivastava in order to prove a generalization of the Representation Theorem of Kreitz‐Weihrauch for Borel measurable functions on computable metric spaces: such functions are Borel measurable on a certain finite level, if and only if they admit a realizer on Baire space of the same quality. This Representation Theorem enables us to introduce a realizer reducibility for functions on metric spaces and we can extend the completeness result to this reducibility. Besides being very useful by itself, this reducibility leads to a new and effective proof of the Banach‐Hausdorff‐Lebesgue Theorem which connects Borel measurable functions with the Baire functions. Hence, for certain metric spaces the class of Borel computable functions on a certain level is exactly the class of functions which can be expressed as a limit of a pointwise convergent and computable sequence of functions of the next lower level. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
19.
Franz Strobl 《Journal of Theoretical Probability》1995,8(4):825-831
The empirical discrepancy is defined as a supremum over a class of functions of a collection of centered sample averages.
For uncountable classes the discrepancy need not be measurable, and distributional assertions can become dependent on the
structure of the underlying probability space. This paper shows that one such assertion—the reversed sub-martingale property—is
valid when interpreted in terms of measurable cover functions for the canonical model, but that it can fail in other constructions
of the underlying model. 相似文献
20.
关于依测度拓扑收敛 总被引:1,自引:0,他引:1
吐尔德别克 《应用泛函分析学报》2004,6(1):5-9
给出了τ-可测算子的依测度收敛的充要条件和Hilbert空间内依测度收敛的充要条件. 相似文献