Document Details Document Type : Article In Journal  Document Title : Tightness of probability measures on function spaces Tightness of probability measures on function spaces   Subject : Mthematics  Document Language : English  Abstract : Let CE = C ([0 1], E) be the Banach space, with the supremum norm, of all continuous functions f from the unit interval [0 1] into the Banach space E. If E = R we put CR = C. Function spaces under consideration are equipped with their Borel σ-field. This paper deals with the tightness property of some classes of probability measures (p.m) on the function space CE. We will be concerned mainly with the specific cases E = R, E = C and more generally E a separable Banach space. We give sufficient conditions for tightness by extending and strengthening the conditions developed by Prohorov in connection with limit theorems of stochastic processes. In the general case of a separable Banach space E, the property of tightness will be settled under conditions of different nature from those of Prohorov. Finally weak convergence of p.m on CE will be established under the condition of weak convergence of their finite dimensional distributions. This extends a similar result valid in the space C. © 2008 Elsevier Inc. All rights reserved.  ISSN : 0022-247X  Journal Name : Journal of Mathematical Analysis and Applications  Volume : 354  Issue Number : 1  Publishing Year : 2009 AH 2009 AD  Number Of Pages : 4  Article Type : Article  Added Date : Tuesday, October 13, 2009  Researchers Researcher Name (Arabic) Researcher Name (English) Researcher Type Dr Grade Email لخضر مبارك بلعيد مزياني مزياني Researcher Doctorate mezianilakhdar@hotmail.com Files File Name Type Description  23402.pdf pdf Abstract Back To Researches Page