TL;DR
This paper investigates the conditions under which a control measure exists for a family of measures on a Boolean algebra, providing new criteria and characterizations for such measures and related properties.
Contribution
It introduces a necessary and sufficient condition for the existence of a control measure and a new criterion for weak compactness of additive set functions.
Findings
Established a necessary and sufficient condition for control measures
Derived a new criterion for weak compactness of additive set functions
Provided several related results on measures on Boolean algebras
Abstract
In this paper we discuss the existence of a control measure for a family of measures on a Boolean algebra. We obtain a necessary and sufficient condition and several related results, including a new criterion for weak compactness for additive set functions on an algebra of sets.
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