  In this paper we adapt the well-estabilished $\Gamma$-calculus techniques to
the context of $RCD(K,\infty)$ spaces, proving Bobkov's local isoperimetric
inequality and, when $K$ is positive, the Gaussian isoperimetric inequality in
this class of spaces. The proof relies on the measure-valued $\Gamma_2$
operator introduced by Savar\'e.
