Convergence Of Measures Research Articles

A Two-Dimentional Discrete Limit Theorem in the Space of Analytic Functions for Mellin Transforms of the Riemann Zeta-Function

In the paper, a two-dimentional discrete limit theorem in the sense of weak convergence of probability measures in the space of analytic functions for Mellin transforms of the Riemann zeta-function on the critical line is obtained.

A General Discrete Limit Theorem in the Space of Analytic Functions for the Matsumoto Zeta-Function

Previous article Next article A General Discrete Limit Theorem in the Space of Analytic Functions for the Matsumoto Zeta-FunctionR. Kačinskaitė and A. LaurinčikasR. Kačinskaitė and A. Laurinčikashttps://doi.org/10.1137/S0040585X97983195PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractA modified discrete limit theorem in the sense of the weak convergence of probability measures in the space of analytic functions for the Matsumoto zeta-function is proved.[1] Google Scholar[2] Google Scholar[3] R. Kačinskaitė, A discrete limit theorem for the Matsumoto zeta-function on the complex plane, Lithuanian Math. J., 40 (2000), pp. 364–378. LMJTD6 0363-1672 CrossrefGoogle Scholar[4] R. Kačinskaitė, A discrete limit theorem for the Matsumoto zeta-function in the space of analytic functions, Lithuanian Math. J., 41 (2001), pp. 344–350. LMJTD6 0363-1672 CrossrefGoogle Scholar[5] R. Kačinskaitė, A discrete limit distribution for the Matsumoto zeta-function in the space of meromorphic functions, Lithuanian Math. J., 42 (2002), pp. 37–53. LMJTD6 0363-1672 CrossrefGoogle Scholar[6] Google Scholar[7] A. Laurinčikas, Limit theorems for the Matsumoto zeta-function, J. Théorie Nombres Bordeaux, 8 (1996), pp. 143–158. CrossrefGoogle Scholar[8] A. Laurinčikas, On limit distribution of the Matsumoto zeta-function. II, Lithuanian Math. J., 36 (1996), pp. 371–387. LMJTD6 0363-1672 CrossrefGoogle Scholar[9] A. Laurinčikas, On limit distribution of the Matsumoto zeta-function, Acta Arith., 79 (1997), pp. 31–39. AARIA9 0065-1036 CrossrefGoogle Scholar[10] A. Laurinčikas, On the Matsumoto zeta-function, Acta Arith., 84 (1998), pp. 1–16. AARIA9 0065-1036 CrossrefGoogle Scholar[11] Google Scholar[12] K. Matsumoto, On the magnitude of asymptotic probability measures of Dedekind zeta-functions and other Euler products, Acta Arith., 60 (1991), pp. 125–147. AARIA9 0065-1036 CrossrefGoogle Scholar[13] Google Scholar[14] Yu. V. Prokhorov, Convergence of random processes and limit theorems in probability theory, Theory Probab. Appl., 1 (1956), pp. 157–214. TPRBAU 0040-585X LinkGoogle Scholar[15] Google ScholarKeywordslimit distributionMatsumoto zeta-functionrandom elementprobability measureweak convergence Previous article Next article FiguresRelatedReferencesCited ByDetails Volume 52, Issue 3| 2008Theory of Probability & Its Applications371-542 History Submitted:09 November 2004Published online:27 August 2008 InformationCopyright © 2008 Society for Industrial and Applied MathematicsKeywordslimit distributionMatsumoto zeta-functionrandom elementprobability measureweak convergencePDF Download Article & Publication DataArticle DOI:10.1137/S0040585X97983195Article page range:pp. 523-531ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Narrow Convergence in Spaces of Set-Valued Measures

Summary. We prove an analogue of Topsoe's criterion for relative compactness of a family of probability measures which are regular with respect to a family sets. We consider measures whose values are compact convex sets in a locally convex linear topological space. Introduction. Let T be an abstract set, K a family of subsets of T, and (E;F) a dual pair of real vector spaces, with E endowed with the weak topology (E;F). Let cc(E;F) be the set of all convex compact non-empty subsets of E, and f M+(T;K;cc(E;F)) the set of K-inner regular positive set-valued measures defined on a -fieldB of subsets of T and with values in cc(E;F). We denote by M+(T;K) the set ofK-inner regular non-negative measures defined on B provided with the topology of weak convergence. Prokhorov (11) has proved that if T is a Polish space andB the set of Borel subsets, then the relatively compact subsets of M+(T;K) are precisely the tight ones. But this result is not valid for all topological space (see e.g. (5), (10), (18)). In (16) Topsoe has characterized the relatively compact subsets of M+(T;K) in general situations. Before and after Topsoe's paper there were others (e.g. (1), (3), (18), (5)-(10)). In this paper we generalize to the space f

A note on the weak convergence of probability measures in the D[0,1] space

Let τ be a regular metric as defined below for the D = D [ 0 , 1 ] space. Even when ( D , τ ) is not a separable and complete metric space we show (i) that the usual conditions on a sequence of probability measures in ( D , τ ) ensures its weak convergence and (ii) that Prohorov's theorem in ( D , τ ) can be derived as a consequence of our results.

A Joint Limit Theorem for Laplace Transforms of the Riemann Zeta–Function

In the paper, a joint limit theorem in the sense of weak convergence of probability measures on the complex plane for Laplace transforms of the Riemann zetafunction is obtained.

A Joint Discrete Limit Theorem in the Space of Meromorphic Functions for General Dirichlet Series

A joint discrete limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for general Dirichlet series is proved.

Choquet weak convergence of capacity functionals of random sets

The results in this paper are about the convergence of capacity functionals of random sets. The motivation stems from asymptotic aspects in inference and decision-making with coarse data in biostatistics, set-valued observations, as well as connections between random sets with several emerging uncertainty calculi in intelligent systems such as fuzziness, belief functions and possibility theory. Specifically, we study the counter-part of Billingsley’s Portmanteau Theorem for weak convergence of probability measures, namely, convergence of capacity functionals of random sets in terms of Choquet integrals.

On topological properties of the Choquet weak convergence of capacity functionals of random sets

In view of the recent interests in random sets in information technology, such as models for imprecise data in intelligent systems, morphological analysis in image processing, we present, in this paper, some contributions to the foundation of random set theory, namely, a complete study of topological properties of capacity functionals of random sets, generalizing weak convergence of probability measures. These results are useful for investigating the concept of Choquet weak convergence of capacity functionals leading to tractable criteria for convergence in distribution of random sets. The weak topology is defined on the space of all capacity functionals on R d . We show that this topological space is separable and metrizable.

A limit theorem for the Hurwitz zeta function with an algebraic irrational parameter

A limit theorem in the sense of weak convergence of probability measures in the space of analytic functions for the Hurwitz zeta function with an algebraic irrational parameter is obtained. Bibliography 6 titles.

Limit theorems for the Laplace transform of the Riemann zeta-function

In this paper, limit theorems in the sense of the weak convergence of probability measures on the complex plane as well as in the space of analytic functions for the Laplace transform of the square of the Riemann zeta-function are obtained.

Portmanteau theorem for unbounded measures

We prove an analogue of the portmanteau theorem on weak convergence of probability measures allowing measures which are unbounded on an underlying metric space but finite on the complement of any Borel neighbourhood of a fixed element.

The joint distribution of the Riemann zeta - function

In the paper the asymptotic distribution of (|ζ(s)|,ζ(s)), where ζ(s) is the Riemann zeta - function, in the sense of weak convergence of probability measures is considered. For this, the continuity theorems for probability measures on ℝ × ℂ are used. Some aspects of the dependence of |ζ(s)| and ζ(s) are also discussed.

Limit theorems for the Estermann zeta-function. II

Abstract A limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for the Estermann zeta-function is obtained.

ON THE DERIVATIVES OF ZETA-FUNCTIONS OF CERTAIN CUSP FORMS, II

The discrete universality of the derivative and logarithmic derivative of zeta-functions of normalized eigenforms is obtained. This is used to estimate the number of zeros of the derivatives in the critical strip. For the proof the method of functional limit theorems in the sense of weak convergence of probability measures is applied.

Value Distribution of General Dirichlet series. VI

In the paper a limit theorem in the sense of weak convergence of probability measures on the complex plane for a new class of general Dirichlet series is obtained.

Joint value distribution of the matsumoto zeta-functions

The Matsumoto zeta-function is defined by a polynomial Euler product and is a generalization of classical zeta-functions. In this article, a joint limit theorem in the sense of the weak convergence of probability measures on the complex plane for the Matsumoto zeta-functions is proved.

The nonlinear membrane model: a Young measure and varifold formulation

We establish two new formulations of the membrane problem by working in the space of W 1,p Γ0 (Ω,R 3 )-Young measures and W 1,p Γ0 (Ω,R 3 )-varifolds. The energy functional related to these formulations is obtained as a limit of the 3d formulation of the behavior of a thin layer for a suitable variational convergence associated with the narrow convergence of Young measures and with some weak convergence of varifolds. The interest of the first formulation is to encode the oscillation informations on the gradients minimizing sequences related to the classical formulation. The second formulation moreover accounts for concentration effects.

Limit theorems for the Estermann zeta-function. I

A limit theorem in the sense of the weak convergence of probability measures on the complex plane for the Estermann zeta-function is proved.

Joint discrete limit theorems in the space of analytic functions for general Dirichlet series

We prove joint discrete limit theorems in the sense of weak convergence of probability measures in the space of analytic functions for general Dirichlet series.

A Joint Limit Theorem on the Complex Plane for General Dirichlet Series

We prove a joint two-dimensional limit theorem in the sense of weak convergence of probability measures on the complex plane for general Dirichlet series.