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. 
@article{MZM_1997_62_1_a13,
     author = {A. V. Uglanov},
     title = {Four counterexamples to the {Fubini} theorem},
     journal = {Matemati\v{c}eskie zametki},
     pages = {124--127},
     publisher = {mathdoc},
     volume = {62},
     number = {1},
     year = {1997},
     language = {ru},
     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/