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1.
Theoretically speaking, there are four kinds of possibilities to define the random conjugate space of a random locally convex module. The purpose of this paper is to prove that among the four kinds there are only two which are universally suitable for the current development of the theory of random conjugate spaces. In this process, we also obtain a somewhat surprising and crucial result: if the base (Ω, F , P ) of a random normed module is nonatomic then the random normed module is a totally disconnected topological space when it is endowed with the locally L0 -convex topology.  相似文献   

2.
In this paper we consider an enlargement of the notion of the probabilistic normed space. For this new class of probabilistic normed spaces we give some topological properties. By using properties of the probabilistic norm we prove some differential and integral properties of functions with values into probabilistic normed spaces. As special cases, results for deterministic and random functions can be obtained.   相似文献   

3.
This paper concerns the construction and regularity of a transition (probability) function of a non-homogeneous continuous-time Markov process with given transition rates and a general state space. Motivating from a lot of restriction in applications of a transition function with continuous (in t≥0) and conservative transition rates q(t, x, Λ), we consider the case that q(t,x,Λ) are only required to satisfy a mild measurability (in t≥0) condition, which is a generalization of the continuity condition. Under the measurability condition we construct a transition function with the given transition rates, provide a necessary and sufficient condition for it to be regular, and further obtain some interesting additional results.  相似文献   

4.
Some stability results for the functional equations of Cauchy and Jensen in probabilistic setting are proved by using the fixed point method.  相似文献   

5.
Summary We prove that the maximal conjugate and Hilbert operators are not bounded from the real Hardy space H1 to L1, where the underlying spaces may be over T or R. We also draw corollaries for the corresponding spaces over T2 and R2.  相似文献   

6.
The left-definite Hilbert spaces for singular Sturm-Liouville problems of the limit-circle type are explicitly constructed. The construction only uses an explicit form of the left-definite boundary conditions, together with a principle solution and a non-principle solution of the differential equation involved.  相似文献   

7.
In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The result is also an extersion of a known theorem in the corresponding non-random case.  相似文献   

8.
We prove that the metric characterization of real normed spaces obtained by T. Oikhberg and H. Rosenthal can be obtained without a continuity assumption provided that the space is at least two-dimensional. In order to get this improvement we first need to understand the exceptional one-dimensional case.  相似文献   

9.
ABSTRACT

We study the random weak ergodic property of infinite products of mappings acting on complete metric spaces. Our results describe an aspect of the asymptotic behaviour of random infinite products of such mappings. More precisely, we show that in appropriate spaces of sequences of operators there exists a subset, which is a countable intersection of open and everywhere dense sets, such that each sequence belonging to this subset has the random weak ergodic property. Then we show that several known results in the literature can be deduced from our general result.  相似文献   

10.
We consider the Orlicz-Kantorovich modules L M (?,m) associated with a complete Boolean algebra ?, an N-function M, and a measure m defined on ? and taking values in the algebra L 0 of all measurable real functions. We obtain an analytic representation of the continuous L 0-valued homomorphisms defined on such modules.  相似文献   

11.
In this paper we consider elliptic equations of order 2m in a bounded domainQ є R n with boundaryδQ and nonlocal conditions relating the traces of the solution and its derivatives on (n − 1)-dimensional smooth manifolds Γ i (∪ i =∂δQ) to their values on some compact setFQ, whereFδQ ≠ Φ. The Fredholm solvability of these problems in the weight spacesV p, a /l+2m (Q) is proved for arbitrary 1<p <∞. Translated fromMatematicheskie Zametki, Vol. 67, No. 6, pp. 882–898, June, 2000. This research was supported by the Russian Foundation for Basic Research under grant No. 99-01-00028.  相似文献   

12.
For weighted sums Σj = 1najVj of independent random elements {Vn, n ≥ 1} in real separable, Rademacher type p (1 ≤ p ≤ 2) Banach spaces, a general weak law of large numbers of the form (Σj = 1najVjvn)/bnp 0 is established, where {vn, n ≥ 1} and bn → ∞ are suitable sequences. It is assumed that {Vn, n ≥ 1} is stochastically dominated by a random element V, and the hypotheses involve both the behavior of the tail of the distribution of |V| and the growth behaviors of the constants {an, n ≥ 1} and {bn, n ≥ 1}. No assumption is made concerning the existence of expected values or absolute moments of the {Vn, n >- 1}.  相似文献   

13.
Several fixed point theorems for symmetric spaces are proved. Then these theorems are used in symmetric PPM-space to prove and generalize Theorem 6 of [T.L. Hicks, B.E. Rhoades, Fixed point theory in symmetric spaces with applications to probabilistic spaces, Nonlinear Anal. 36 (1999) 331-344].  相似文献   

14.
姚云飞 《大学数学》2002,18(5):49-53
在赋范线性空间中考察下列几类泛函方程( ) f(x) g(y) =h(x+y) ,  ( ) f(x+y) =f(x) f(y) ,  ( ) f(x+y) =f(x) +f(y) +ag(x) g(y)的性质与解以及彼此之间的关系 .  相似文献   

15.
16.
We utilize S. Park's maximal element theorem in this paper to prove the existence theorems of solutions of the complementarity problems for multivalued monotone operator in Banach spaces.  相似文献   

17.
中心目的是详细廉政论在随机共轭空间理论形成过程中所经历的三个阶段的工作,尤其指出了这三个阶段工作之间的联系及本质差别;给出了强有界、拓扑有界及几乎处处有界随机线性泛函之间的关系;亦指出了在概率赋范空间上线性算子理论研究中目前存在的不足.  相似文献   

18.
Jensen's inequality is extended to metric spaces endowed with a convex combination operation. Applications include a dominated convergence theorem for both random elements and random sets, a monotone convergence theorem for random sets, and other results on set-valued expectations in metric spaces and on random probability measures.  相似文献   

19.
This paper continues our earlier work on random quadratic forms. We show that if continuity conditions for a family of quadratic forms holds uniformly on an index set, generalized focal/conjugate point signature approximation results hold. We then apply these results to obtain continuity of thenth focal point in a random (robust) setting.  相似文献   

20.
The paper considers upper semicontinuous behavior in distribution of sequences of random closed sets. Semiconvergence in distribution will be described via convergence in distribution of random variables with values in a suitable topological space. Convergence statements for suitable functions of random sets are proved and the results are employed to derive stability statements for random optimization problems where the objective function and the constraint set are approximated simultaneously. The author is grateful to two anonymous referees for helpful suggestions.  相似文献   

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