  We consider a continuous function $f$ on a domain in $\mathbf C^n$ satisfying
the inequality that $|\bar \partial f|\leq |f|$ off its zero set. The main
conclusion is that the zero set of $f$ is a complex variety.
  We also obtain removable singularity theorem of Rado type for J-holomorphic
maps. Let $\Omega$ be an open subset in $\mathbf C$ and let $E$ be a closed
polar subset of $\Omega$. Let $u$ be a continuous map from $\Omega$ into an
almost complex manifold $(M,J)$ with $J$ of class $C^1$. We show that if $u$ is
J-holomorphic on $\Omega\setminus E$ then it is J-holomorphic on $\Omega$.
