共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
Wilfred E. Boykin 《School science and mathematics》1995,95(2):78-82
The author has extended Pick's theorem for simple closed polygonal regions to unions of simple closed polygonal regions–a topic that is manageable for middle grade students. From sets of data including numbers of boundary points and numbers of interior points, students are guided to discover Pick's theorem. Additionally, with the author's creation of crossing points, Pick's theorem is extended to include areas of other polygonal regions. The article is developed along lines of the 1989 Standards of the NCTM in the use of data tables which lead to the discovery of a formula. 相似文献
3.
《Annals of Pure and Applied Logic》2022,173(2):103058
We study Kim-independence over arbitrary sets. Assuming that forking satisfies existence, we establish Kim's lemma for Kim-dividing over arbitrary sets in an NSOP1 theory. We deduce symmetry of Kim-independence and the independence theorem for Lascar strong types. 相似文献
4.
Ivan N. Soskov 《Mathematical Logic Quarterly》1996,42(1):469-480
The main result proved in the paper is that on every recursive structure the intrinsically hyperarithmetical sets coincide with the relatively intrinsically hyperarithmetical sets. As a side effect of the proof an effective version of the Kueker's theorem on definability by means of infinitary formulas is obtained. Mathematics Subject Classification: 03D70, 03D75. 相似文献
5.
《复变函数与椭圆型方程》2012,57(4):325-332
In the present paper, we answer two questions raised by Jarnicki and Pflug: First, we show by a counterexample that the Hartogs-Bochner theorem is no longer true for non-separated Riemann domains. Secondly, we generalize a structure theorem of Dloussky, which examines the extension of singularity sets contained in analytic hypersurfaces, to non-separated Riemann domains. Moreover, our method yields a new proof of Dloussky's original result. 相似文献
6.
Takeshi Yamaguchi 《Mathematical Logic Quarterly》1997,43(1):45-48
Productive sets are sets which are “effectively non recursively enumerable”. In the same spirit, we introduce a notion of “effectively nonrecursive sets” and prove an effective version of Post's theorem. We also show that a set is recursively enumerable and effectively nonrecursive in our sense if and only if it is effectively nonrecursive in the sense of Odifreddi [1]. 相似文献
7.
We use an idea of countable separability of points and sets in topological spaces to prove results on intersection of measurable multifunctions and an implicit function theorem. We generalize or extend in part some well known Himmelberg's theorems. 相似文献
8.
Jacob S. Christiansen 《Advances in Mathematics》2012,229(2):1180-1204
In this paper, we generalize Szeg?'s theorem for orthogonal polynomials on the real line to infinite gap sets of Parreau–Widom type. This notion includes Cantor sets of positive measure. The Szeg? condition involves the equilibrium measure which in turn is absolutely continuous. Our approach builds on a canonical factorization of the M-function and the covering space formalism of Sodin–Yuditskii. 相似文献
9.
Two new eigenvalue inclusion sets for tensors are established. It is proved that the new eigenvalue inclusion sets are tighter than that in Qi's paper “Eigenvalues of a real supersymmetric tensor”. As applications, upper bounds for the spectral radius of a nonnegative tensor are obtained, and it is proved that these upper bounds are sharper than that in Yang's paper “Further results for Perron–Frobenius theorem for nonnegative tensors”. And some sufficient conditions of the positive definiteness for an even‐order real supersymmetric tensor are given. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
10.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1998,326(4):433-436
We prove results which are parallel to Lempert's theorem on the plurisbharmonic Green function of a convex domain for the extremal plurisubharmonic function relative to two convex domains. Namely, its sublevel sets are convex and the region between the two domains is foliated by complex curves on which the relative extremal function is harmonic. 相似文献
11.
《Annals of Pure and Applied Logic》2023,174(9):103317
We show that Morley's theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of equivalence relations obtained by countable intersections of projective sets in several models of set theory. Our methods include random and Cohen forcing, Woodin cardinals and Inner Model Theory. 相似文献
12.
Deng-Feng Li 《Fuzzy Optimization and Decision Making》2011,10(1):45-58
The Atanassov’s intuitionistic fuzzy (IF) set theory has become a popular topic of investigation in the fuzzy set community.
However, there is less investigation on the representation of level sets and extension principles for interval-valued intuitionistic
fuzzy (IVIF) sets as well as algebraic operations. In this paper, firstly the representation theorem of IVIF sets is proposed
by using the concept of level sets. Then, the extension principles of IVIF sets are developed based on the representation
theorem. Finally, the addition, subtraction, multiplication and division operations over IVIF sets are defined based on the
extension principle. The representation theorem and extension principles as well as algebraic operations form an important
part of Atanassov’s IF set theory. 相似文献
13.
Local Spherical Contact Distribution Function And Local Mean Densities For Inhomogeneous Random Sets
In this paper we provide definitions for the local mean volume and mean surface densities of an inhomogeneous random closed set A theorem which relates the local spherical contact distribution function with the local surface and volume density is proven. Sufficient conditions on the regularity of the random set involved to satisfy the assumptions of the theorem are provided, based on Coarea Formula. These conditions are satisfied by a wide class of inhomogeneous random sets, relevant for applications, like some kinds of Boolean Models, for which explicit expressions for the local volume and surface densities are also provided 相似文献
14.
We prove a necessary and sufficient condition for the existence of edge list multicoloring of trees. The result extends the Halmos–Vaughan generalization of Hall's theorem on the existence of distinct representatives of sets. © 2003 Wiley Periodicals, Inc. J Graph Theory 42: 246–255, 2003 相似文献
15.
Jorge Galindo 《Advances in Mathematics》2004,188(1):51-68
Rosenthal's theorem describing those Banach spaces containing no copy of ?1 is extended to topological groups replacing ?1-basis by interpolation sets in the sense of Hartman and Ryll-Nardzewsky (Colloq. Math. 12 (1964) 23-39). This extension provides a characterization of those locally compact groups containing no interpolation sets and of those locally compact groups which respect compactness, i.e, such that every Bohr compact subset is compact. The approach followed in this paper sheds some light on other questions related to the duality theory of non-Abelian locally compact groups. 相似文献
16.
New theorems of Helly type are proved concerning the intersection of convex cones with a common vertex or, equivalently, the intersection of sets on a sphere which are convex in the sense of Robinson. The proofs of these theorems are based on a lemma which is a spherical analog and generalization of Radon's theorem. 相似文献
17.
I. A. Lavrov 《Algebra and Logic》1996,35(3):164-171
A new approach to the study of creative sets using the notion of a table is offered. Making use of tables conforming to recursively
enumerable sets, novel properties of creative sets are established. Harrington's theorem on the definability of creative sets
in the lattice of recursively enumerable sets is proved, and we reprove Lachlan's theorem which states that one of the factors
in a direct product of creative sets is again creative.
Supported by RFFR grant No. 93-01-16014.
Translated fromAlgebra i Logika, Vol. 35, No. 3, pp. 294–307, May–June, 1996. 相似文献
18.
Hadwiger’s transversal theorem gives necessary and suffcient conditions for a family of convex sets in the plane to have a line transversal. A higher dimensional version was obtained by Goodman, Pollack and Wenger, and recently a colorful version appeared due to Arocha, Bracho and Montejano. We show that it is possible to combine both results to obtain a colored version of Hadwiger's theorem in higher dimensions. The proofs differ from the previous ones and use a variant of the Borsuk-Ulam theorem. To be precise, we prove the following. Let F be a family of convex sets in ? d in bijection with a set P of points in ? d?1. Assume that there is a coloring of F with suffciently many colors such that any colorful Radon partition of points in P corresponds to a colorful Radon partition of sets in F. Then some monochromatic subfamily of F has a hyperplane transversal. 相似文献
19.
知识规律与规律的属性扰动 总被引:1,自引:0,他引:1
By employing the knowledge(R-element equivalence class)in one direction Srough sets and dual of one direction S-rough sets,the concept of knowledge law is given;the generation theorem of knowledge law,the excursion theorem of knowledge law,and the attribute disturbance discernible theorem of knowledge law are proposed.Knowledge law is a new characteristic of S-rough sets. 相似文献
20.
An integral representation theorem for outer continuous and inner regular belief measures on compact topological spaces is elaborated under the condition that compact sets are countable intersections of open sets (e.g. metric compact spaces). Extreme points of this set of belief measures are identified with unanimity games with compact support. Then, the Choquet integral of a real valued continuous function can be expressed as a minimum of means over the sigma-core and also as a mean of minima over the compact subsets. Similarly, for bounded measurable functions, the Choquet integral is expressed as min of means over the core, we prove in addition that it is a mean of infima over the compact subsets. Then, we obtain Choquet–Revuz' measure representation theorem and introduce the Möbius transform of a belief measure. An extension to locally compact and sigma-compact topological spaces is provided. 相似文献