  In this paper, we study the amoeba volume of a given $k-$dimensional generic
analytic variety $V$ of the complex algebraic torus $(\C^*)^n$. When $n\geq
2k$, we show that $V$ is algebraic if and only if the volume of its amoeba is
finite. In this precise case, we establish a comparison theorem for the volume
of the amoeba and the coamoeba. Examples and applications to the $k-$linear
spaces will be given.
