Some results on differentiable measures

Connections are described between various differentiability properties of measures on locally convex spaces. In particular, it is proved that every analytic measure is quasi-invariant, and every quasi-invariant measure is absolutely continuous with respect to some analytic measure. It is proved that for stable measures continuity in some direction implies infinite differentiability, and even analyticity in this direction when $\alpha\geqslant1$. A solution is presented for a problem posed by Aronszajn (RZh.Mat., 1977, 5B557).
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