  We prove that in any metric space $(X,d)$ the singular integral operators
{equation*} T^k_{\mu,\ve}(f)(x)=\int_{X\setminus
B(x,\varepsilon)}k(x,y)f(y)d\mu (y).{equation*} converge weakly in some dense
subspaces of $L^2(\mu)$ under minimal regularity assumptions for the measures
and the kernels.
