  The measure concentration property of an mm-space $X$ is roughly described as
that any 1-Lipschitz map on $X$ to a metric space $Y$ is almost close to a
constant map. The target space $Y$ is called the screen. The case of
$Y=\mathbb{R}$ is widely studied in many literature (see \cite{gromov},
\cite{ledoux}, \cite{mil2}, \cite{milsch}, \cite{sch}, \cite{tal}, \cite{tal2}
and its reference). M. Gromov developed the theory of measure concentration in
the case where the screen $Y$ is not necessarily $\mathbb{R}$ (cf.
\cite{gromovcat}, {gromov2}, \cite{gromov}). In this paper, we consider the
case where the screen $Y$ is a nonpositively curved manifolds. We also show
that if the screen $Y$ is so big, then the mm-space $X$ does not concentrate.
