Geodesic
Four counterexamples to the Fubini theorem
Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 124-127.

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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 $\sigma$-bounded measures need not be a $\sigma$-bounded measure. 
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     title = {Four counterexamples to the {Fubini} theorem},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a13/}
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A. V. Uglanov. Four counterexamples to the Fubini theorem. Matematičeskie zametki, Tome 62 (1997) no. 1, pp. 124-127. http://geodesic.mathdoc.fr/item/MZM_1997_62_1_a13/

[1] Uglanov A. V., “Teorema Fubini dlya vektornykh mer”, Matem. sb., 181:3 (1990), 423–432 | Zbl

[2] Neve Zh., Matematicheskie osnovy teorii veroyatnostei, Mir, M., 1969 | Zbl