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In this note, we shall prove that the sum and the product of an algebraicnumber $\alpha$ by the \textit{Liouville constant}$L=\sum_{j=1}^{\infty}10^{-j!}$ is a $U$-number with type equals to the degreeof $\alpha$ (with respect to $\mathbb{Q}$). Moreover, we shall have that  $\max\{w^{\ast}_n(\alpha L),w^{\ast}_n(\alpha + L)\}\leq 2m^2n+m-1$, for$n=1,...,m-1$.

Transcendence Measures for some $U_m$-numbers related to Liouville's constant