Geodesic
Change of variables in a~multiple Lebesgue integral
Matematičeskie zametki, Tome 14 (1973) no. 1, pp. 39-48.

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Necessary and sufficient conditions are found for a change of variables in a multiple Lebesgue integral for a class of quasibijective (one-to-one everywhere except on a set whose image has measure zero) mappings in the Euclidean space $R^n$. 
@article{MZM_1973_14_1_a4,
     author = {I. V. Orlov},
     title = {Change of variables in a~multiple {Lebesgue} integral},
     journal = {Matemati\v{c}eskie zametki},
     pages = {39--48},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_1_a4/}
}
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I. V. Orlov. Change of variables in a~multiple Lebesgue integral. Matematičeskie zametki, Tome 14 (1973) no. 1, pp. 39-48. http://geodesic.mathdoc.fr/item/MZM_1973_14_1_a4/