摘要
This paper introduces the concept of orthogonal vector measures, and gives the Yosida-Hewittdecomposition theorem for this kind of vector measures. The major results are(a) Any orthogonal vector measure can gain it countable additivity by enlarging its domain;(b) Every orthogonal vector measure can be represented as the sum of two orthogonal vectormeasures, one of which is countably additive, and the other is purely finitely additive. Furthermore,these vector measures are completely perpendicular to each other.
This paper introduces the concept of orthogonal vector measures, and gives the Yosida-Hewittdecomposition theorem for this kind of vector measures. The major results are(a) Any orthogonal vector measure can gain it countable additivity by enlarging its domain;(b) Every orthogonal vector measure can be represented as the sum of two orthogonal vectormeasures, one of which is countably additive, and the other is purely finitely additive. Furthermore,these vector measures are completely perpendicular to each other.
