  When the \textit{martingale representation property} holds, we call any local
martingale which realizes the representation a \textit{representation process}.
There are two properties of the \textit{representation process} which can
greatly facilitate the computations under the \textit{martingale representation
property}. Actually, on the one hand, the \textit{representation process} is
not unique and there always exists a \textit{representation process} which is
locally bounded and has pathwisely orthogonal components outside of a
predictable thin set. On the other hand, the jump measure of a
\textit{representation process} satisfies the \textit{finite predictable
constraint}. In this paper, we give a detailed account of these two properties.
As application, we will prove that, under the \textit{martingale representation
property}, the \textit{full viability} of an expansion of market information
flow implies the \textit{drift multiplier assumption}.
