Geodesic
On the theory of set-valued maps of bounded variation of one real variable
Sbornik. Mathematics, Tome 189 (1998) no. 5, pp. 797-819

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(Set-valued) maps of bounded variation in the sense of Jordan defined on a subset of the real line and taking values in metric or normed linear spaces are studied. A structure theorem (more general than the Jordan decomposition) is proved for such maps; an analogue of Helly's selection principle is established. A compact set-valued map into a Banach space that is a map of bounded variation (or a Lipschitz or an absolutely continuous map) is shown to have a continuous selection of bounded variation (respectively, Lipschitz or absolutely continuous selection). 
@article{SM_1998_189_5_a7,
     author = {V. V. Chistyakov},
     title = {On the theory of set-valued maps of  bounded variation of one real variable},
     journal = {Sbornik. Mathematics},
     pages = {797--819},
     publisher = {mathdoc},
     volume = {189},
     number = {5},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_5_a7/}
}
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V. V. Chistyakov. On the theory of set-valued maps of  bounded variation of one real variable. Sbornik. Mathematics, Tome 189 (1998) no. 5, pp. 797-819. http://geodesic.mathdoc.fr/item/SM_1998_189_5_a7/