Geodesic
A Criterion for Contiguity of Quasiconcave Functions
Matematičeskie zametki, Tome 70 (2001) no. 5, pp. 780-786.

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Quasiconcave functions $\rho _0$ and $\rho _1$ belong to the same scale if there exist quasiconcave functions $\psi _0$ and $\psi _1$ and numbers $0\theta _01$, $0\theta _11$ such that $\rho _0=\psi _0^{1-\theta _0}\psi _1^{\theta _0}$ and $\rho _1=\psi _0^{1-\theta _1}\psi _1^{\theta _1}$. We establish a criterion for such functions to belong to the same scale up to equivalence. This criterion is obtained in terms of nodes of the corresponding linear-constant step-functions. It turns out that nodes must be equivalent to sequences. 
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V. I. Ovchinnikov; A. S. Titenkov. A Criterion for Contiguity of Quasiconcave Functions. Matematičeskie zametki, Tome 70 (2001) no. 5, pp. 780-786. http://geodesic.mathdoc.fr/item/MZM_2001_70_5_a12/

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