Abstract
In this paper we study signed measures. Our main results are as follows: the Fubini theorem is not true in the general case; the Jordan parts of a transition measure are not necessarily transition measures; the operation of taking the Jordan parts does not necessarily commute with multiplying by the initial measure; the product of σ-bounded measures need not be a σ-bounded measure.
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References
A. V. Uglanov, “The Fubini theorem for vector measures”,Mat. Sb. [Math. USSR-Sb.]181, No. 3, 423–432 (1990).
J. Neveu,Bases mathématiques du calcul des probabilités Masson et Cie, Paris (1964).
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Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 124–127, July, 1997.
Translated by S. S. Anisov
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Uglanov, A.V. Four counterexamples to the Fubini theorem. Math Notes 62, 104–107 (1997). https://doi.org/10.1007/BF02356071
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DOI: https://doi.org/10.1007/BF02356071