TY - JOUR

T1 - On a unifying approach to decomposition theorems of Yosida-Hewitt type

AU - Basile, Achille

AU - Bukhvalov, Alexander V.

N1 - Basile, A. On a unifying approach to decomposition theorems of Yosida-Hewitt type / A. Basile, A. V. Bukhvalov // Annali di Matematica Pura ed Applicata. - 1997. - Volume 173, Issue 1. - P. 107-125.

PY - 1997/1/1

Y1 - 1997/1/1

N2 - In this paper we deal with a very general form of the Yosida-Hewitt theorem on the decomposition of measures into countably additive («normal») and purely finitely additive («antinormal») parts. It expands a previous one by the authors with the aim of joining two different standpoints to the Yosida-Hewitt type theorems. The first goes back to the original publication defining the «antinormal» part as a certain disjoint complement to the «normal» one. The second approach goes deeper and characterizes this disjoint complement intrinsically i.e. as a measure, functional or operator which is equal to zero on a huge set. These two points of view are common for the publications connected, respectively, with measure theory and theory of vector lattices; the second allows important applications. The unification of these approaches gives an opportunity to derive new information in the case of vector measures. We have taken the opportunity of this paper also to furnish a survey of the topic.

AB - In this paper we deal with a very general form of the Yosida-Hewitt theorem on the decomposition of measures into countably additive («normal») and purely finitely additive («antinormal») parts. It expands a previous one by the authors with the aim of joining two different standpoints to the Yosida-Hewitt type theorems. The first goes back to the original publication defining the «antinormal» part as a certain disjoint complement to the «normal» one. The second approach goes deeper and characterizes this disjoint complement intrinsically i.e. as a measure, functional or operator which is equal to zero on a huge set. These two points of view are common for the publications connected, respectively, with measure theory and theory of vector lattices; the second allows important applications. The unification of these approaches gives an opportunity to derive new information in the case of vector measures. We have taken the opportunity of this paper also to furnish a survey of the topic.

KW - theorems of Yosida-Hewitt type

KW - SCOPUS

UR - http://www.scopus.com/inward/record.url?scp=33845190712&partnerID=8YFLogxK

U2 - 10.1007/BF01783464

DO - 10.1007/BF01783464

M3 - Article

AN - SCOPUS:33845190712

VL - 173

SP - 107

EP - 125

JO - Annali di Matematica Pura ed Applicata

JF - Annali di Matematica Pura ed Applicata

SN - 0373-3114

IS - 1

ER -