Density measures and additive property

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    Abstract

    We consider a certain class of normalized positive linear functionals on l which extend the Cesàro mean. We study the set of its extreme points and it turns out to be the set of linear functionals constructed from free ultrafilters on natural numbers N. Also, regarding them as finitely additive measures defined on all subsets of N, which are often called density measures, we study a certain additivity property of such measures being equivalent to the completeness of the Lp-spaces on such measures. Particularly a necessary and sufficient condition for such a density measure to have this property is obtained.

    Original languageEnglish
    Pages (from-to)184-203
    Number of pages20
    JournalJournal of Number Theory
    Volume176
    DOIs
    Publication statusPublished - 2017 Jul 1

    Fingerprint

    Linear Functionals
    Finitely Additive Measure
    Ultrafilter
    Additivity
    Lp Spaces
    Extreme Points
    Natural number
    Completeness
    Necessary Conditions
    Subset
    Sufficient Conditions
    Class

    Keywords

    • Additive property
    • Asymptotic density
    • Cesàro mean
    • Density measure
    • Finitely additive measure

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

    Density measures and additive property. / Kunisada, Ryoichi.

    In: Journal of Number Theory, Vol. 176, 01.07.2017, p. 184-203.

    Research output: Contribution to journalArticle

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