Geodesic
On the uniqueness of hypermeasures in Euclidean spaces
Izvestiya. Mathematics, Tome 7 (1973) no. 6, pp. 1423-1432 
V. A. Zhil'tsov. On the uniqueness of hypermeasures in Euclidean spaces. Izvestiya. Mathematics, Tome 7 (1973) no. 6, pp. 1423-1432. http://geodesic.mathdoc.fr/item/IM2_1973_7_6_a8/
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     author = {V. A. Zhil'tsov},
     title = {On the uniqueness of hypermeasures in {Euclidean} spaces},
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     url = {http://geodesic.mathdoc.fr/item/IM2_1973_7_6_a8/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper questions of uniqueness of axiomatic measures in Euclidean spaces are studied. The basic result is that an axiomatic measure agrees with Hausdorff measure under certain suppositions about the axiomatic measure and the $\sigma$-field on which it is defined.

[1] Federer H., “Area $k$-dimentional non-parametric surface in $k+1$ cartisien space”, Trans. Amer. Math. Soc., 77 (1964), 374–407 | MR

[2] Danford N., Shvarts Dzh., Lineinye operatory, IL, M., 1962

[3] Rogers C. A., Hausdorff measure, Cambridge Univ. Press, London, 1970 | MR

[4] Federer H., “The $(\varnothing,k)$ rectifiable subsets of $n$-space”, Trans. Amer. Math. Soc., 62 (1947), 114–192 | DOI | MR | Zbl

[5] Stepanov W., “Sur le conditions de léxistence de la differential total”, Matem. sb., 32 (1925), 511 | Zbl

[6] Saks S., Teoriya integrala, IL, M., 1949

[7] Vitushkin A. G., “Dokazatelstvo polunepreryvnosti sverkhu variatsii mnozhestv”, Dokl. AN SSSR, 166:5 (1966), 1022–1026 | MR