We showed the existence of singular adapted metrics for any  codimension one singular hyperbolic set  with respect to a $C^1 vector field on finite dimensional compact manifolds without using quadradic forms. Looking at the measures of a system,  we  provided a Kingman-like Theorem for an arbitrary finite measure  assuming some conditions in any metric space, and we give necessary conditions to guarantee  the existence of invariant measures in locally compact and separable metric spaces for continuous proper maps. Moreover, we use the Perron-Frobenius operator and the techniques developed here to obtain other criteria to guarantee  the existence of invariant measures for continuous maps (not necessarily a proper maps) in  locally compact separable metric spaces.