  The purpose of this note is to show that a finitely generated graded module
$M$ over $S=k[x_1,\ldots,x_n]$, $k$ a field, is sequentially Cohen-Macaulay if
and only if its arithmetic degree ${\rm adeg}(M)$ agrees with ${\rm
adeg}(F/{\rm gin}_{revlex}(U))$, where $F$ is a graded free $S$-module and $M
\cong F/U$. This answers positively a conjecture of Lu and Yu from 2016.
