Some results on strong limit theorems for (LB)-space-valued random variables

Xaingchen Wang, M. Bhaskara Rao and Deli Li

Statistics & Probability Letters, 1995, vol. 23, issue 3, 247-251

Abstract: Let E be a strict (LB)-space, i.e., a strict inductive limit of separable Banach spaces E1 [subset of] E2 [subset of] ... One of the results proved in this is the following. Let Xn, n [greater-or-equal, slanted] 1 be a sequence of independent identically distributed (i.i.d.) random variables taking values in E. If the Strong law of large numbers holds for this sequence, i.e., (1/m)[summation operator]i = 1m Xi, m [greater-or-equal, slanted] 1 converges almost surely, then there exists n [greater-or-equal, slanted] 1 such that each Xi takes values in En almost surely.

Keywords: Convergence; with; probability; one; Strict; (LB)-space; Strong; law; of; large; numbers (search for similar items in EconPapers)
Date: 1995
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0167-7152(94)00121-N
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:23:y:1995:i:3:p:247-251

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().