  In this paper, we consider (random) sampling of signals concentrated on a
bounded Corkscrew domain $\Omega$ of a metric measure space, and reconstructing
concentrated signals approximately from their (un)corrupted sampling data taken
on a sampling set contained in $\Omega$. We establish a weighted stability of
bi-Lipschitz type for a (random) sampling scheme on the set of concentrated
signals in a reproducing kernel space. The weighted stability of bi-Lipschitz
type provides a weak robustness to the sampling scheme, however due to the
nonconvexity of the set of concentrated signals, it does not imply the unique
signal reconstruction. From (un)corrupted samples taken on a finite sampling
set contained in $\Omega$, we propose an algorithm to find approximations to
signals concentrated on a bounded Corkscrew domain $\Omega$. Random sampling is
a sampling scheme where sampling positions are randomly taken according to a
probability distribution. Next we show that, with high probability, signals
concentrated on a bounded Corkscrew domain $\Omega$ can be reconstructed
approximately from their uncorrupted (or randomly corrupted) samples taken at
i.i.d. random positions drawn on $\Omega$, provided that the sampling size is
at least of the order $\mu(\Omega) \ln (\mu(\Omega))$, where $\mu(\Omega)$ is
the measure of the concentrated domain $\Omega$. Finally, we demonstrate the
performance of proposed approximations to the original concentrated signal when
the sampling procedure is taken either with small density or randomly with
large size.
