共查询到20条相似文献,搜索用时 0 毫秒
1.
Abhijit Dasgupta 《Proceedings of the American Mathematical Society》2001,129(8):2441-2443
Using a technique developed by Louveau and Saint Raymond, we find the complexity of the space of probability measures in the Borel hierarchy: if is any non-Polish Borel subspace of a Polish space, then , the space of probability Borel measures on with the weak topology, is always true , where is the least ordinal such that is .
2.
M. G. Nadkarni 《Proceedings Mathematical Sciences》1990,100(3):203-220
A necessary and sufficient condition is given for a Borel automorphism on a standard Borel space to admit an invariant probability
measure. 相似文献
3.
In the Type-2 Theory of Effectivity, one considers representations of topological spaces in which infinite words are used as “names” for the elements they represent. Given such a representation, we show that probabilistic processes on infinite words, under which each successive symbol is determined by a finite probabilistic choice, generate Borel probability measures on the represented space. Conversely, for several well-behaved types of space, every Borel probability measure is represented by a corresponding probabilistic process. Accordingly, we consider probabilistic processes as providing “probabilistic names” for Borel probability measures. We show that integration is computable with respect to the induced representation of measures. 相似文献
4.
该文把A.P.Singh关于一类齐次微分多项式级的结果推广到更一般的微分多项式。并证明了:如果Q(f)≠0是圆内有限正级亚纯函数f的身长分多项式,则f^(k0Q(f)的Borel点必是f的Borel点,其中K0满足0≤K0≤min{K:f^(k)出现在Q(f)中}。 相似文献
5.
L. Báez-Duarte 《Journal of Theoretical Probability》1993,6(1):33-56
We prove two central limit theorems for real identically distribution random variables where the distribution is a complex-valued Borel measure . The results involve the weak convergence of the suitably scaledn-fold convolution of certain complex atomic or absolutely continuous measures of spectral radius 1 to ahypergaussian measure whose Fourier-Stieltjes transform is exp(–2 for a positive integer . The proof uses a generalization of the method of characteristic functions. Counter-examples are given to rather more general statements that had appeared previously in the literature. This research arose in connection with problems related to general tauberian theorems on the line for complexvalued summability methods which are discussed at the end of the paper. Some interesting examples are given generalizing well-known theorems related to Euler and Borel summability. 相似文献
6.
T. Gal 《Journal of Optimization Theory and Applications》1985,45(4):577-589
Consider an extreme point (EP)x
0 of a convex polyhedron defined by a set of linear inequalities. If the basic solution corresponding tox
0 is degenerate,x
0 is called a degenerate EP. Corresponding tox
0, there are several bases. We will characterize the set of all bases associated withx
0, denoted byB
0. The setB
0 can be divided into two classes, (i) boundary bases and (ii) interior bases. For eachB
0, there is a corresponding undirected graphG
0, in which there exists a tree which connects all the boundary bases. Some other properties are investigated, and open questions for further research are listed, such as the connection between the structure ofG
0 and cycling (e.g., in linear programs). 相似文献
7.
Beverly L. Brechner Kazuhiro Kawamura 《Proceedings of the American Mathematical Society》2001,129(2):617-620
We prove that the homeomorphism group of each one of a collection of continua constructed in a paper by the first author (Trans. Amer. Math. Soc. 121 (1966), 516-548) is one dimensional. This answers a question posed in that paper.
8.
《Optimization》2012,61(1):81-101
In this article, the well-known minimax theorems of Wald, Ville and von Neumann are generalized under weaker topological conditions on the payoff function f and/or extended to the larger set of the Borel probability measures, instead of the set of mixed strategies. 相似文献
9.
X. H. Gong 《Journal of Optimization Theory and Applications》1995,86(3):609-630
One of the important problems of vector optimization concerns the density of the set of positive proper minimal points in the set of minimal points. We use the concepts of dentable point and approximating cones to derive sufficient conditions guaranteeing that the set of minimal points is contained in the closure of the set of positive proper minimal points. The result can be applied to obtain a density result for the unit ball in 1
p
, 1<p<+, which does not follow from any other well-known density theorem.The author would like to thank Professor W. T. Fu for helpful comments. Moreover, the author is grateful to Professor H. P. Benson and the referees for valuable remarks and suggestions concerning a previous draft of this paper. 相似文献
10.
Density of periodic points, invariant measures and almost equicontinuous points of cellular automata
Revisiting the notion of μ-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure μ by iterations of such automata converges in Cesàro mean to an invariant measure μc. Moreover the dynamical system (cellular automaton F, invariant measure μc) has still the μc-almost equicontinuity property and the set of periodic points is dense in the topological support of the measure μc. We also show that the density of periodic points in the topological support of a measure μ occurs for each μ-almost equicontinuous cellular automaton when μ is an invariant and shift ergodic measure. Finally using most of these results we give a non-trivial example of a couple (μ-equicontinuous cellular automaton F, shift and F-invariant measure μ) such that the restriction of F to the topological support of μ has no equicontinuous points. 相似文献
11.
Klaus Bichteler 《manuscripta mathematica》1972,7(3):215-249
A theory of integration is described which subsumes as special cases Bourbaki's integration of Radon measures and Caratheodory's integration of set functions.Supported partly by NSF Grant GP-20541 相似文献
12.
13.
We prove that, under a mild summability condition on the growth of the derivative on critical orbits any piecewise monotone interval map possibly containing discontinuities and singularities with infinite derivative (cusp map) admits an ergodic invariant probability measures which is absolutely continuous with respect to Lebesgue measure. 相似文献
14.
E. B. Jensen K. Kiêu H. J. G. Gundersen 《Annals of the Institute of Statistical Mathematics》1990,42(3):445-461
Recently, a new set of fundamental stereological formulae based on isotropically oriented probes through fixed points have been derived, the so-called nucleator estimation principle (cf. Jensen and Gundersen (1989, J. Microsc., 153, 249–267)). In the present paper, it is shown how a model-based version of these formulae leads to stereological estimators of reduced moment measures of stationary and isotropic random sets in
n
. 相似文献
15.
V. L. Selivanov 《Algebra and Logic》2005,44(2):95-108
We deal with the Borel and difference hierarchies in the space P of all subsets of endowed with the Scott topology. (The spaces P and 2
coincide set-theoretically but differ topologically.) We look at the Wadge reducibility in P. The results obtained are applied to the problem of characterizing 1-terms t which satisfy C = t(
1
0
) for a given Borel-Wadge class C. We give its solution for some levels of the Wadge hierarchy, in particular, all levels of the Hausdorff difference hierarchy. Finally, we come up with a discussion of some relevant facts and open questions.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 173–197, March–April, 2005. 相似文献
16.
On the set of limit points of the partial sums of series rearranged by a given divergent permutation
Roman Witua 《Journal of Mathematical Analysis and Applications》2010,362(2):542-552
We give a new characterization of divergent permutations. We prove that for any divergent permutation p, any closed interval I of (the 2-point compactification of ) and any real number sI, there exists a series ∑an of real terms convergent to s such that I=σap(n) (where σap(n) denotes the set of limit points of the partial sums of the series ∑ap(n)). We determine permutations p of for which there exists a conditionally convergent series ∑an such that ∑ap(n)=+∞. If the permutation p of possesses the last property then we prove that for any and there exists a series ∑an convergent to α and such that σap(n)=[β,+∞]. We show that for any countable family P of divergent permutations there exist conditionally convergent series ∑an and ∑bn such that any series of the form ∑ap(n) with pP is convergent to the sum of ∑an, while for every pP. 相似文献
17.
Randall Dougherty R. Daniel Mauldin Andrew Yingst 《Transactions of the American Mathematical Society》2007,359(12):6155-6166
Let be the Bernoulli measure on the Cantor space given as the infinite product of two-point measures with weights and . It is a long-standing open problem to characterize those and such that and are topologically equivalent (i.e., there is a homeomorphism from the Cantor space to itself sending to ). The (possibly) weaker property of and being continuously reducible to each other is equivalent to a property of and called binomial equivalence. In this paper we define an algebraic property called ``refinability' and show that, if and are refinable and binomially equivalent, then and are topologically equivalent. Next we show that refinability is equivalent to a fairly simple algebraic property. Finally, we give a class of examples of binomially equivalent and refinable numbers; in particular, the positive numbers and such that and are refinable, so the corresponding measures are topologically equivalent.
18.
Fons van Engelen 《Proceedings of the American Mathematical Society》1996,124(8):2589-2598
We provide an example of a zero-dimensional (separable metric) absolute Borel set which is not homogeneous, but whose square admits the structure of a topological group. We also construct a zero-dimensional absolute Borel set such that is a homogeneous non-group but is a group. This answers questions of Arhangel'skii and Zhou.
19.
Nilson C. Bernardes Jr. 《Proceedings of the American Mathematical Society》2005,133(12):3473-3483
Given a metrizable compact topological -manifold with boundary and a metric compatible with the topology of , we prove that ``most' continuous functions are non-sensitive at ``most' points of but are sensitive at every point of an infinite set which is dense in the set of all periodic points of . We also establish some results concerning sets of periodic points and non-wandering points.
20.
The aim of this work is to investigate the integrability properties of the maximal operator Mu,associated with a non-doubling measure μ defined on Rn. We start by establishing for a wide class of radial and increasing measures μ that Mu is bounded on all the spaces Lu^p(R^n),P〉1.Also,we show that there is a radial and increasing measure p for which Mμ does not map Lμ^p(R^n) into weak Lμ^p(R^n),1≤p〈∞. 相似文献