On one class of extreme extensions of a measure - Tarashchans'kii, M. T. (Ukrains’kyi Matematychnyi Zhurnal, 2010)
We consider a relationship between two sets of extensions of a finite finitely additive measure μ defined on an algebra B of sets to a broader algebra A. These sets are the set ex S_μ of all extreme extensions of the measure μ and the set H_μ of all extensions defined as λ(A) = μ(h(A)), A ∈ A, where μ is a quotient measure on the algebra B/μ of the classes of μ-equivalence and h: A →B/μ is a homomorphism extending the canonical homomorphism B to B/μ. We study the properties of extensions from H_μ and present necessary and sufficient conditions for the existence of these extensions, as well as the conditions under which the sets ex S_μ and H_μ coincide.