Modes of ideal continuity of (\ell)-group-valued measures

Boccuto, Antonıo; Dimitriou, Xenofon

doi:10.12988/imf.2013.13088

Cited by 2 publications

(1 citation statement)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This concept has been studied even in topological spaces (see e.g. Das, 2012;Das & Ghosal, 2011;Lahiri & Das, 2005;Lahiri & Das, 2007/2008 and in ( )-groups (see also , 2013bBoccuto, Dimitriou, & Papanastassiou, 2010b, 2012a, 2012b, 2012dBoccuto, Dimitriou, Papanastassiou, & Wilczyński, 2012, 2013. This notion has been several applications in the very recent literature.…”

Section: Introductionmentioning

confidence: 99%

Ideal Limit Theorems and Their Equivalence in $(\ell)$-Group Setting

Boccuto¹,

Dimitriou²

2013

JMR

Self Cite

View full text Add to dashboard Cite

We prove some equivalence results between limit theorems for sequences of ( )-group-valued measures, with respect to order ideal convergence. A fundamental role is played by the tool of uniform ideal exhaustiveness of a measure sequence already introduced for the real case or more generally for the Banach space case in our recent papers, to get some results on uniform strong boundedness and uniform countable additivity. We consider both the case in which strong boundedness, countable additivity and the related concepts are formulated with respect to a common order sequence and the context in which these notions are given in a classical like setting, that is not necessarily with respect to a same (O)-sequence. We show that, in general, uniform ideal exhaustiveness cannot be omitted. Finally we pose some open problems.

show abstract