Geodesic
A Remark on Disintegrations With Almost All Components Non -Additive
Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 786-788

Voir la notice de l'article provenant de la source Cambridge University Press

We extend a theorem of L. E. Dubins on “purely finitely additive disintegrations” of measures (cf. [4]) and apply this result to the disintegrations of extremal Gibbs states with respect to the asymptotic algebra enlarging another result of L. E. Dubins on the symmetric coin tossing game.We recall the following definition of L. E. Dubins (cf. [3], [4]): Let (X , , μ) be a measure space, a sub σ-algebra of . A real function σx (A), is called a measurable-disintegration of μ if: (i) ∀x ∊ X , σx(.) is a finitely additive measure . (ii) ∀A ∊ , σ. (A) is constant on each -atom. (iii) For each A ∊ , σ. (A) is measurable with respect to the completion of by μ and (iv) σx(B) = 1 if x ∊ B ∊ . 
Dang-Ngoc, Nghiem. A Remark on Disintegrations With Almost All Components Non -Additive. Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 786-788. doi: 10.4153/CJM-1979-071-0
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