Probability measure satisfying curvature-dimension

Question

Assume that the non-compact $n$-dimensional Riemannian manifold $M$ satisfies a curvature-dimension $\mathrm{CD}(K,N)$, $K \le 0$, with respect to a measure $\mu = e^{-V} d\mathrm{Vol}$; i.e. \begin{equation*} \mathrm{Ric} + \mathrm{Hess} V - \frac{\nabla V \otimes \nabla V}{N - n} \ge Kg. \end{equation*} I wonder if it possible to have $\mu$ as a probability measure? The only example of $\mathrm{CD}(K,N)$ in this non-compact case I know is from the monograph of Villani - example 14.10: \begin{equation*} \mu(dx) = \cosh^{N-1} \left(\sqrt{\frac{|K|}{N-1}}x\right)dx\end{equation*} which is clearly not normalizable.