Density measures and additive property

Ryoichi Kunisada

doi:10.1016/j.jnt.2016.12.013

Density measures and additive property

Ryoichi Kunisada

Research output: Contribution to journal › Article › peer-review

7 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 L^p-spaces on such measures. Particularly a necessary and sufficient condition for such a density measure to have this property is obtained.

Original language	English
Pages (from-to)	184-203
Number of pages	20
Journal	Journal of Number Theory
Volume	176
DOIs	https://doi.org/10.1016/j.jnt.2016.12.013
Publication status	Published - 2017 Jul 1

Keywords

Additive property
Asymptotic density
Cesàro mean
Density measure
Finitely additive measure

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jnt.2016.12.013

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AB - 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.

KW - Additive property

KW - Asymptotic density

KW - Cesàro mean

KW - Density measure

KW - Finitely additive measure

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JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Density measures and additive property

Abstract

Keywords

ASJC Scopus subject areas

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