A homogeneous measure exists on any compactum in $\mathbf{R}^n$
Doklady Akademii Nauk, Tome 278 (1984) no. 4, pp. 783-786.

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     author = {A. L. Volberg and S. V. Konyagin},
     title = {A homogeneous measure exists on any compactum in $\mathbf{R}^n$},
     journal = {Doklady Akademii Nauk},
     pages = {783--786},
     publisher = {mathdoc},
     volume = {278},
     number = {4},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DAN_1984_278_4_a2/}
}
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A. L. Volberg; S. V. Konyagin. A homogeneous measure exists on any compactum in $\mathbf{R}^n$. Doklady Akademii Nauk, Tome 278 (1984) no. 4, pp. 783-786. http://geodesic.mathdoc.fr/item/DAN_1984_278_4_a2/