Geodesic
On translates of convex measures
Sbornik. Mathematics, Tome 188 (1997) no. 2, pp. 227-236 Cet article a éte moissonné depuis la source Math-Net.Ru

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The following alternative is proved for a convex Radon measure $\mu$, on a locally convex space $X$ and for an arbitrary direction $h\in X$: either $\mu$ is differentiable in the direction $h$ in the sense of Skorokhod and $\|\mu _h-\mu \|\geqslant 2-2e^{-\frac 12\|d_h\mu \|}$, or $\mu$ and $\mu _{th}$ are mutually singular for all $t\in \mathbb R\setminus \{0\}$. 
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     author = {E. P. Krugova},
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     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_2_a2/}
}
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E. P. Krugova. On translates of convex measures. Sbornik. Mathematics, Tome 188 (1997) no. 2, pp. 227-236. http://geodesic.mathdoc.fr/item/SM_1997_188_2_a2/

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