  Let ${\mathfrak H}_A$, ${\mathfrak H}_B$, and ${\mathfrak H}$ be Hilbert
spaces. Let $A$ be a linear relation from ${\mathfrak H}$ to ${\mathfrak H}_A$
and let $B$ be a linear relation from ${\mathfrak H}$ to ${\mathfrak H}_B$. If
there exists an operator $Z \in \mathbf{B}({\mathfrak H}_B,{\mathfrak H}_A)$
such that $ZB \subset A$, then $B$ is said to dominate $A$. This notion plays a
major role in the theory of Lebesgue type decompositions of linear relations
and operators. There is a strong connection to the majorization and
factorization in the well-known lemma of Douglas, when put in the context of
linear relations. In this note some aspects of the lemma of Douglas are
discussed in the context of linear relations and the connections with the
notion of domination will be treated.
